In this work, temperature field, residual stress, and strain field of two-fused-silica substrate welding by femtosecond laser pulses were simulated by ANSYS Workbench (a software of finite element analysis) using a transient thermal model together with a static structural model. A Gaussian heat source was periodically deposited at the interface of the samples and was moved at a constant velocity perpendicular to the optical propagation direction. The maximum residual stress was just 16.474 KPa at a time of 20 s through a simulation analysis. This was not sufficient to cause cracks in the fused silica. In addition, the influence of a magnetic field on the welding process was studied. The value of the residual stress and strain apparently decreased with an external magnetic field. In a real experiment, the maximum bonding strength reached 76.6 MPa under the same conditions as in simulation