A swept volume is a useful tool for solving various types of interference problems. Previous works have concentrated on sweeping an object along an arbitrary path, that results in complex algorithms. This paper concerns the volume swept by translating an object along a linear path. After analyzing the structure of the swept volume, we present an incremental algorithm for constructing a swept volume. Our algorithm takes O(n² *.alpha.(n)+T_c) time where n is the number of vertices in the original object and T_c is time for handling face cycles.