We present in this paper a Bayesian CAD system for robotic applications. We address the problem of the propagation of geometric uncertainties, and how to take into account this propagation when solving inverse problems. The methodology used to represent and handle uncertainties using conditional probability distributions on the system's parameters and the sensor measurements is presented. It may be seen as a generalization of constraint-based approaches in which we explicitly model geometric uncertainties. Using this methodology, a constraint is represented by a probability distribution instead of a simple equality or inequality. Numerical algorithms used to apply this methodology are also described. Using an example, we show how to apply our approach by providing simulation results using our CAD system.