Introduction Solid oxide fuel cells (SOFCs) are an efficient all solid-state power generation device and an important choice for achieving the energy goals. The existing shortcomings like low high-temperature strength, structural reliability, and short service life of SOFCs restrict the commercialization of SOFCs. The core component of SOFC, i.e., the positive-electrolyte-negative (PEN) multilayer composite ceramic electrode plate that works in a redox environment for a long time and bears the cyclic thermal stress caused by multiple starts and stops of the SOFC stack should have a good mechanical strength. The common anode material for SOFC is nickel oxide-yttria-stabilized zirconia (NiO-YSZ) porous ceramic. The NiO-YSZ anode has some problems such as alternating high and low temperature redox, carbon deposition, impurity poisoning, and Ni particle growth during operation, thus leading to the deterioration of the mechanical properties of the anode. It is thus of great significance to evaluate the mechanical properties of the NiO-YSZ anode for SOFCs and evolute the degradation over service time. However, the excessive clamping force can lead to the fragmentation of the entire specimen due to the thin thickness of NiO-YSZ anode and the brittleness of the material. It is difficult for conventional tensile tests to achieve the evaluation of the mechanical strength of the NiO-YSZ anode and PEN components. The small punch test (SPT) is a testing technique that uses micro-sized specimens to obtain the mechanical strength of materials without the need to clamp the specimens. This paper focused on the homogeneous NiO-YSZ anode material of planar SOFC and conducted multiple sets of SPTs. In addition, a method was also proposed to evaluate the mechanical strength of anode NiO-YSZ ceramic component of planar SOFCs using SPT. Methods The initial experimental material was planar anode-supported SOFC multilayer PEN plate, which did not yet put into service and prepared by a tape-casting method. The anode, electrolyte, and cathode materials were NiO-YSZ, YSZ, and LSM (strontium-doped lanthanum manganate)-YSZ, respectively. The plate-shaped PEN was cut into circular specimens with a radius of R=5 mm. The cathode, barrier layer, and electrolyte layer of the specimen were removed by mechanical polishing. The initial thickness t0 of the NiO-YSZ specimen was ultimately controlled to be (0.380±0.010) mm. The SPT adopted a self-developed testing machine with a self-designed SPT clamp. The experiment was controlled by displacement loading at a constant loading rate of 0.02 mm/min. The specimen underwent deformation until failure under the stamping of the punch and loading ball. The load and displacement data were collected by sensors and the load-displacement curve was drawn. The surface and fracture morphology of the specimen were observed by scanning electron microscopy (SEM). The mechanical properties of NiO-YSZ anode (i.e., elastic modulus, characteristic strength, and Weibull modulus) were obtained via the experimental results and mechanical modeling based on an inverse finite element method and the Weibull failure probability model. Results and discussion The load-displacement curve of SPT of NiO-YSZ has three characteristic stages and three load characteristic values P1, P2, and Pm. Based on the fracture observation by SEM, different loading stages correspond to the process of crack initiation and propagation in NiO-YSZ sample, and P1 is determined as a fracture load of the specimen. The elastic modulus of NiO-YSZ anode is determined to be 40 GPa through a reverse finite element method, and the maximum tensile stress of the specimen occurs at the center of the lower surface when the displacement reaches its maximum value (i.e.,149.16 MPa). The corresponding mechanical model was developed, and a formula for calculating the tensile strengths of NiO-YSZ anode specimens was proposed. Under the same conditions, the maximum tensile stress of the theoretically calculated for the specimen is 152.29 MPa, which is only 2.1% different from the numerical simulation result. The reason for the deviation ise due to the simplification of the contact process during theoretical modeling, while the finite element method can more closely simulate the deformation between the loading ball and the specimen during the experimental process to obtain a more accurate numerical solution. The ultimate tensile strengths of 22 NiO-YSZ specimens were calculated through the theoretical formulas. The ultimate tensile strength exhibits a certain degree of dispersion due to the inherent properties of brittle ceramic materials. Therefore, the Weibull failure probability model was used to statistically analyze the results, and the characteristic strength of ultimate tensile strength of NiO-YSZ anode material is 160.88 MPa, with the Weibull modulus of 7.61. This achieves the evaluation of strength, reliability and uniformity of NiO-YSZ anode material. Conclusions The load-displacement curve of SPT of NiO-YSZ anode had three load characteristic values P1, P2, and Pm. Based on the SEM observation, different experimental stages corresponded to the crack initiation and propagation stages of the specimen. After the load reaches P1, some cracks appeared at the center of the lower surface of the specimen, and P1 was determined as a material fracture load. A mechanical theoretical model for the SPT of ceramic materials was proposed. The Weibull statistical results of the tensile strength of NiO-YSZ anode were obtained by four different methods, and a formula for calculating the tensile strength of NiO-YSZ ceramic specimens suitable for SPT was obtained. The mechanical strength of NiO-YSZ anode material had a dispersibility, and the elastic modulus of the research object NiO-YSZ anode material was determined to be 40 GPa through the reverse finite element method. A method for evaluating the mechanical strength of SOFC electrode ceramic components based on SPT was proposed. The statistical analysis was conducted on 22 sets of experimental results, yielding a characteristic tensile strength of 160.90 MPa with a Weibull modulus (m) of 7.61 for this material.