The care and rehabilitation of individuals after lower limb amputation presents a substantial and growing socioeconomic challenge. Clinical outcome is closely linked to successful functional rehabilitation with a prosthetic limb, which depends upon comfortable prosthetic limb - residual limb load transfer. Despite early interest in the 1980s, the amputated limb has received considerably less attention in computational biomechanical analysis than other subjects, such as arthroplasty. This systematic literature review investigates the state of the art in residual limb finite element analysis published since 2000. The identified studies were grouped into the following categories: (1) residuum-prosthesis interface mechanics; (2) residuum soft tissue internal mechanics; (3) identification of residuum tissue characteristics; (4) proposals for incorporating FEA into the prosthesis fitting process; (5) analysis of the influence of prosthetic componentry concepts to improve load transfer to the residuum, such as the monolimb and structural socket compliance; and (6) analysis of osseointegrated (OI) prostheses. The state of the art is critically appraised in order to form recommendations for future modeling studies in terms of geometry, material properties, boundary conditions, interface models, and relevant but un-investigated issues. Finally, the practical implementation of these approaches is discussed.