Two computational techniques are presented for Computer-Aided Design (CAD) and Machining (CAM) of parametrically defined surfaces. One technique deals with construction of offset surfaces. An algorithm is presented that would allow detection and removal of the closed loop on the offset surface due to its self-intersection. The second computational technique presented deals with contouring of parametric surfaces. The technique presented allows for optimal generation of planar contour lines. The results are applied to Numerical Control (NC) machining of surfaces.