Mobility analysis is an important step in the conceptual design of flexure systems. It involves identifying directions with relatively compliant motion (freedoms) and directions with relatively restricted motion (constraints). This paper proposes a deterministic framework for mobility analysis of wire flexure systems based on characterizing a kinetostatic vector field known as “load flow” through the geometry. A hypothesis is proposed to identify constraints and freedoms based on the relationship between load flow and the flexure geometry. This hypothesis is mathematically restated to formulate a matrix-based reduction technique that determines flexure mobility computationally. Several examples with varying complexity are illustrated to validate the efficacy of this technique. This technique is particularly useful in analyzing complex hybrid interconnected flexure topologies, which may be nonintuitive or involved with traditional methods. This is illustrated through the computational mobility analysis of a bio-inspired fiber reinforced elastomer pressurized with fluids. The proposed framework combines both visual insight and analytical rigor, and will complement existing analysis and synthesis techniques.