The robust stability analysis of Constrained Model Predictive Control (CMPC) for linear time invariant and openloop stable processes is the main topic of this paper. Based on the CMPC algorithm, the feedback controller is a piecewise linear operator because of the constraints. This piecewise linear operator can be thought of as an array of linear feedback controllers in parallel, handling different types of predicted active constraint situations. Each term in the linear operator corresponding to the predicted active constraint situation can be decomposed to have an uncertainty block. Hence, the linear operator can be written as a linear closed-form with uncertainty block inside. According to the linear robust stability analysis method, the robust stability of CMPC can be analyzed and the computer aided off-line tuning for the stability of CMPC can also be developed by solving a minimum maximum problem based on the stability analysis method. Some examples are given to show the feasibility of the analysis and tuning methods.