The elastic-plastic deformation evolution, stress distribution and tensile fracture behavior during the tensile process of laser non-penetrating lap welded joints of the 301L stainless steel plates with different thicknesses are studied by the numerical analysis methods. The finite element model of laser welded joints is established and the simulated tensile curves of welded joints are in a relatively good agreement with the experimental results. With the increase of tensile load, the plastic deformation of welded specimens extends from the base metal near the weld interface to both of the weld interface and the base metal. In contrast, with the increase of the ratio of weld width to plate thickness, the plastic strain zone of welded specimens extends gradually from the vicinity of weld interface to the base metal. The tensile fracture displacement increases with the increase of plastic deformation zone. Moreover, when the ratio of weld width to plate thickness is higher than 0.75 and the fracture displacement of welded specimens is larger than 5 mm, the fracture strength is relatively high and the shear fracture strength of laser weld is about 794 MPa.