Planning the manufacture of machined parts requires a great deal of geometric reasoning. One of the key steps in this task is the derivation of machinable features from a solid model of the part. Regardless of the approach used for obtaining the features, geometric interactions among the features can create situations where there are several possible feature representations for the same part. This presents a problem in planning the manufacture of the part, since some of these representations may be manufacturable and some may not. This dissertation presents an automatic way of computing alternate feature interpretations using an algebra of feature interactions. The algebra is intended to enable automated process planning systems to decide whether various interpretations of a part as a collection of machinable features are feasible for manufacturing, and among the feasible ones, which is the most appropriate one for manufacturing. Alternate feature interpretations are computed by performing operations in the algebra. Furthermore, various provable properties of the feature algebra aid in resolving several of the feature interactions without even applying the operations in the algebra. The operations in the algebra are defined on the set of all compact, regular, semi-analytic solids. A restricted subset of the algebra has been implemented in a geometric reasoning system, for use with the Protosolid solid modeler and the EFHA process planning system (which were developed earlier at the University of Maryland). We have shown through experiments that computing the operations of the feature algebra as developed in this dissertation is much more efficient than computing them by converting them to quiries to solid modeler.