321 and 410 stainless steels were brazed using 400 W pulsed Nd:YAG laser source with AMS 4777 filler metal for various joint clearances. Optical microscopy and scanning electron microscopy were used to study the microstructure of all specimens. Mechanical properties (microhardness and tensile test) of all specimens were evaluated. The wetting, spreading, and flowing of AMS 4777 filler metal on substrates during this process were modeled using finite volume model. The equations of conservation of mass, conservation of momentum, and conservation of energy were solved in FLUENT software for calculating volume fraction and liquid fraction. AMS 4777 filler metal shows excellent wettability on the 321 and 410 stainless steels. The filler metal and specimens mainly consist of nickel solid solution (Ni), chromium boride (CrB), and nickel boride (Ni3B). The average microhardness for specimens in seam is 492 HV. The tensile strength of specimens changes from 200 up to 480 MPa due to various joint clearances. The higher tensile strength of 321 stainless steel specimens in comparison with 410 stainless steel specimens is due to less wetting angle and more spreading width of filler metal. The simulated results show that this model can be used for predicting geometry of joints at various joint clearances.