Flux balance analysis and constraint based modeling have been successfully used in the past to elucidate the metabolism of single cellular organisms. However, limited work has been done with multicellular organisms and even less with humans. The focus of this paper is to present a novel use of this technique by investigating human nutrition, a challenging field of study. Specifically, we present a steady state constraint based model of skeletal muscle tissue to investigate amino acid supplementation's effect on protein synthesis. We implement several in silico supplementation strategies to study whether amino acid supplementation might be beneficial for increasing muscle contractile protein synthesis. Concurrent with published data on amino acid supplementation's effect on protein synthesis in a post resistance exercise state, our results suggest that increasing bioavailability of methionine, arginine, and the branched-chain amino acids can increase the flux of contractile protein synthesis. The study also suggests that a common commercial supplement, glutamine, is not an effective supplement in the context of increasing protein synthesis and thus, muscle mass. Similar to any study in a model organism, the computational modeling of this research has some limitations. Thus, this paper introduces the prospect of using systems biology as a framework to formally investigate how supplementation and nutrition can affect human metabolism and physiology.