Spinal cord injury patients are under daily risk for developing deep tissue injury which is a severe pressure ulcer that initiates in soft tissues at the bones' proximity. We aimed to formulate a patient-specific biomechanical model that can continuously monitor internal tissue stresses in real time. We adopted a formulation solving an axisymmetric contact problem of a finite-thickness, elastic layer (soft tissue), and a rigid spherical indentor (ischial tuberosity). We utilized finite element analyses to expand the formulation for large deformations. Sensitivity analyses showed that the soft tissue mechanical properties are the most influential factors in this modeling. We then used synthetic surface pressure data and actual surface pressures recorded under the buttocks of five paraplegic wheelchair users to demonstrate clinical feasibility. Output parameters were designed to be simple so that they can be easily interpreted by the user. Specifically, we calculated peak and average internal von Mises stress and stress dose, under each buttock, and also a time-dependent stress asymmetry index, to account for frequency of posture adjustments. Inter-subject variability was higher than the intra-subject variability. The heaviest subject had the highest maximal and average peak internal soft tissue stress. We believe that this method holds a high potential for clinical applications.