A computer program is described which performs symbolic algebra and calculus with vectors and dyadics. Implemented on the MACSYMA algebraic manipulation system, it is intended to be a reasonably complete analysis system for applications such as plasma physics and fluid dynamics. It includes manipulations of dot and cross products; gradient, divergence, curl and Laplacian operators; directional derivatives and outer products. Vector and dyadic equations can be automatically expanded into components for arbitrary orthogonal coordinate systems. Designed primarily for 2-dimensional and 3-dimensional use, the program also has some capability for higher dimensions. The internal structure of the code is discussed with regard to efficiency considerations. Example calculations and execution times are presented.