We describe a numerical method for calculating the magnetohydrodynamic (MHD) spectrum of one-dimensional equilibria with Bow. Due to a general formulation, the spectrum for two different equilibrium geometries, viz. a plane slab and a cylinder, can be investigated. The linearised equations are discretised with a Finite Element Method. This results in a large non-Hermitian matrix eigenvalue problem, which can be solved using standard techniques. We present test cases for the method and new results on the effect of a sheared poloidal flow and a sheared magnetic field on the MHD spectrum. (C) 1997 Elsevier Science B.V.