Engineered products are designed for manufacture using nominal values and tolerances. As such, finished products will more or less satisfy design specifications depending on the actual materials and manufacturing processes used. Design feasibility, therefore, depends on how these variations impact specified constraints. Probabilistic feasibility analysis can be used to extend conventional feasibility analysis. By using moment matching and simulation, the probability of points occurring in the design space can be evaluated. The resulting values establish the limits of feasibility and the amount of feasibility in between. The nature of variation in mechanical design is introduced along with concepts of variation propagation in functions of random variables. Moment matching methods are applied to illustrative cases consisting of deterministic and probabilistic constraint equations, resulting in three dimensional feasibility mappings of each design space.