The development of artificial prosthetic lower limbs aims to improve patient's mobility while avoiding secondary problems resulting from the use of the prostheses themselves. The residual limb is a pressure-sensitive area where skin injuries and pain are more likely to develop. Requirements for adequate prosthetic limbs have now become urgent to improve amputee's quality of life. This study aims to understand how socket design parameters related to geometry can influence pressure distribution in the residual limb. A finite element model was developed to simulate the mechanical loading applied on the residual limb of a below-knee amputee while walking. A sensitivity analysis to socket initial geometry, scaling the socket downward in the horizontal plane, was performed. Recordings include stress levels on the skin and in the residual limb deep soft tissues. Peak stress was reduced by up to 51% with a limited reduction of the socket size. More important scale reduction of the residual limb would lead to possible negative effects, such as stress concentrations in sensitive areas. This result confirms the interest of the prosthetist to develop a well-fitting socket, possibly a little smaller than the residual limb itself, in order to avoid residual limb mobility in the socket that could cause friction and stress concentrations. Non-homogeneous geometrical reductions of the socket should be further investigated.