This paper presents a novel scheme for the use of linear programming to calculate muscle contraction forces in models describing musculoskeletal system biomechanics. Models of this kind are frequently found in the biomechanics literature. In most cases they involve muscle contraction force calculations that are statically indeterminate, and hence use optimization techniques to make those calculations. We present a linear programming optimization technique that solves a two-objective problem with two sequential linear programs. We use the technique here to minimize muscle intensity and joint compression force, since those are commonly used objectives. The two linear program model has the advantages of low computation cost, ready implementation on a micro-computer, and stable solutions. We show how to solve the model analytically in simple cases. We also discuss the use of the dual problem of linear programming to gain understanding of the solution it provides.