A sensitivity analysis methodology based on continuation techniques is applied to chemical engineering processes. The method is based on the trace of the optimal solution path of a process model under multiple model parameter variations of finite magnitude. The first-order stationarity conditions form a system of parameterized nonlinear equations. The solution of the equation set for different values of the parameters is obtained using continuation methods (PITCON). The behavior of the optimal solution path is studied around singular points. Simple tests are used to detect singularities due to violation of the strict complementarity, linear independence constraint qualification or second-order optimality conditions. The example cases involve single and multiple unit models with equation sets of moderate to large size. The method can handle active constraint set changes and can determine the range of model parameter variations in a given direction for which the model is feasible. It can be used to determine the most sensitive unit in a plant for a given disturbance and calculate multiple solutions to the stationarity conditions for the same parameter values.