A finite element (FE) approach is developed to investigate the laser spot welding (LSW) of flat-plate solar absorbers and the stress and distortion fields that develop after fabrication and during operation. Numerical calculations at two different levels are carried out. At a microscopic scale, the details of a spot weld are analyzed. At a macroscopic level, a global approach is used to simulate the joining of the pipeline to the absorber plate and the “restoration” (flattening) process of the absorber. The simulated welding-induced distortion is compared with experimental measurements. The thermomechanical behavior of a solar absorber under working conditions is also studied and operational stresses and the critical locations for structural failure are reported.