We present a numerical study of a square-shape rod-like bonded laser gain medium operating at 1053 nm. The sample is composed of a 5-mm thick Nd-doped phosphate glass bonded to two α-quartz crystals. Owing to this face cooling scheme, the heat generated in the gain medium is effectively reduced, hence resulting in less optical distortions. The simulation of the thermomechanical effects was conducted using COMSOL MultiPhysics® software. Transverse wavefront distortion and birefringence profiles were computed for a given pump mean power. Wavefront and birefringence measurements will be conducted on the bonded sample using a pump-probe setup which is discussed in this paper. These measurements will be presented and weighed with the numerical results.