The Finite Integral method is a numerical method of solving simultaneous differential equations. This paper reviews the technique and explores the solution of some forced vibration problems. Examples 1, 2 and 3 are simple applications designed to illustrate the formulation and to draw comparisons with "exact" classical approaches. The latter part of the paper provides a detailed formulation of a more substantial vibration problem involving the modelling of a "rolling load" system and the girder which supports it. The technique appears to be well-suited to the solution of such problems. It provides a concise computational tool in the analysis of forced vibration problems which are not amenable to solution by such classical techniques as Modal Superposition. It may, of course, be used as an alternative to classical methods and stands alongside the more familiar Finite Difference-based dynamic analysis procedures.