Ascending stairs is challenging following transtibial amputation due to the loss of the ankle muscles, which are critical to human movement. Efforts to improve stair ascent following amputation are hindered by limited understanding of how prostheses and remaining muscles contribute to stair ascent. This study developed a three-dimensional muscle-actuated forward dynamics simulation of amputee stair ascent to identify contributions of individual muscles and passive prosthesis to the biomechanical subtasks of stair ascent. The prosthesis was found to provide vertical propulsion throughout stair ascent, similar to non-amputee plantarflexors. However, the timing differed considerably. The prosthesis also contributed to braking, similar to non-amputee soleus, but to a greater extent. In contrast, the prosthesis was unable to replicate the functions of non-amputee gastrocnemius which contributes to forward propulsion during the second half of stance and leg swing initiation. To compensate, hamstrings and vasti of the residual leg increased their contributions to forward propulsion during the first and second halves of stance, respectively. The prosthesis also contributed to medial control, consistent with the non-amputee soleus but not gastrocnemius. Therefore, prosthesis designs that provide additional vertical propulsion as well as forward propulsion, lateral control and leg swing initiation at appropriate points in the gait cycle could improve amputee stair ascent. However, because non-amputee soleus and gastrocnemius contribute oppositely to many subtasks, it may be necessary to couple the prosthesis, which functions most similarly to soleus, with targeted rehabilitation programs focused on muscle groups that can compensate for gastrocnemius.