Reverse engineering involves digitizing a 3-D model or part, by means of a tactile or non-contact optical sensor, converting the data to a computer aided design (CAD) database description, and manufacturing the part by computer numeric controlled (CNC) machines. A common reverse engineering approach has been to scan the physical model from a single viewpoint to obtain points on a single valued surface and then fit relatively flat B-spline surface patches. This thesis presents a new approach which allows wrap-around B-spline surfaces to be fitted . The approach is demonstrated in the reverse engineering of physical models by employing a 3-D laser scanning system in conjunction with the surface fitting software developed by the author. Accurate surface data is collected by the laser scanner and then input to the surface fitting software. Surface entities such as B-spline and quadric functions are employed to build the CAD model. The CAD model is compatible with commonly used design and manufacturing software packages. The reverse engineering of a bicycle seat and a telephone receiver are used to illustrate the efficiency of the process.