We present a Bayesian CAD modeler for robotic applications. We describe the methodology we use to represent and handle uncertainties using probability distributions on the system parameters and sensor measurements. We address the problem of the propagation of geometric uncertainties and how to take this propagation into account when solving inverse problems. The proposed approach may be seen as a generalization of constraint-based approaches where we express a constraint as a probability distribution instead of a simple equality or inequality. We also describe appropriate numerical algorithms used to apply this methodology. Using an example, we show how to apply our approach by providing simulation results using the implemented CAD modeler.