A vector algorithm for computing the two-dimensional Discrete Cosine Transform (2D-VDCT) is presented. The formulation of 2D-VDCT is stated under the framework provided by elements of multilinear algebra. This algebraic framework provides not only a formalism for describing the 2D-VDCT, but it also enables the derivation by pure algebraic manipulations of an algorithm that is well suited to be implemented in SIMD-vector signal processors with a scalable level of parallelism. The 2D-VDCT algorithm can be implemented in a matrix oriented language and a suitable compiler generates code for our family of STA (Synchronous Transfer Architecture) vector architectures with different amounts of SIMD-parallelism. We show in this paper how important speedup factors are achieved by this methodology.