The incubation effect plays an important role in the process of ultrafast laser ablation and processing. This article investigates the threshold and incubation effect of femtosecond laser ablation of YAG crystals with a wavelength of 1 030 nm. Under the shot of a single pulse, the YAG surface undergoes "mild" ablation, with a smaller ablation aperture and depth; When subjected to multiple pulses, due to the influence of incubation, the ablation threshold significantly decreases with the increase of pulse count and eventually converges to a stable value. This article uses three incubation models to compare and study their fitting effects on the ablation threshold of YAG crystals. Through experiments and fitting, it was found that the ablation threshold under single pulse shot is $ {{F}}_{\mathrm{t}\mathrm{h},1} $=(12.27±3.56) J/cm²; Under the shot of multiple pulses, the saturation incubation threshold is $ {{F}}_{\mathrm{t}\mathrm{h},\mathrm{\infty }} $=(1.82±0.37) J/cm². This study provides a reference for the control of parameters such as energy and pulse number in femtosecond laser precision machining.Femtosecond laser adopts external control mode, achieving precise control of the number of pulses through high-precision function/arbitrary waveform signal generator (DG1000Z) and high-precision electronic shutter. The control of laser power is achieved through the combination of a half-wave plate and a polarizer. The laser beam is focused on the surface of the sample using a microscope objective (NA=0.28) with 10×, and the sample is fixed on a high-precision stage. The surface morphology changes and damage processes can be observed online using a CCD camera. After the YAG crystal was irradiated by laser, the ablation morphology of the sample was observed by optical microscope (KEYENCE VH-Z500) and atomic force microscopy (Dimension ICON), and the diameters of different ablation pits were measured. The ablation threshold was obtained by drawing D²–ln${E}_{{\rm{in}}}$curve for calculating ${E}_{{\rm{th}}}$(N) and $ \mathrm{\omega } $.The incubation coefficient S of Model I and the incubation coefficient k of Model III fitted in this article are similar to other transparent materials reported in the literature, such as quartz and sapphire. The incubation model results obtained are also basically consistent with those in the literature. The incubation coefficient of Model II is about twice that of other materials in the literature, but the correlation coefficient is significantly higher, which fits well with the incubation effect of YAG crystals under multiple pulses. Under low-energy flow density laser irradiation, the material undergoes "mild" ablation. When the energy flow density is high, the material undergoes rapid evaporation and removal. Under the shot of multiple pulses, the incubation effect plays an important role in the ablation process. In dielectric and semiconductor materials, defects can be inherent in the material or caused by external conditions, such as laser induced color centers. As the number of laser irradiation increases, the defect density increases with the number of laser irradiation pulses until it reaches saturation. At the same time, the accumulation of defects will lead to an increase in effective absorption coefficient and a decrease in surface ablation threshold until saturation is reached.We investigate the ablation threshold and incubation effect of YAG crystals under the shot of 1 030 nm femtosecond laser, and experimentally obtains the single pulse ablation threshold. We studied the variation of ablation threshold under multiple pulses and combined three incubation models to investigate the incubation phenomenon under multiple pulses. Among them, Model I is suitable for single pulse ablation threshold fitting, Model II has the best fitting accuracy under multiple pulses, and Model III has the best overall fitting. This study provides parameters and operating conditions for ultra-fast femtosecond laser processing of YAG, providing reference for surface microstructure processing and parameter control of smaller structure.