Systems of finite elements are organized using matrix notation for finite length bearings. Most fluid film bearings have surface areas which can be divided into a grid of elements whose nodes are labeled in matrix form. The resulting equations for nodal pressures are block tridiagonal and the solution is easily obtained with direct methods. Analysis of both general slider and journal bearings is included. The choice of how the film is divided into elements can significantly affect the error involved in the numerical solution and some criteria are developed for optimizing the division scheme. In the analysis of a square squeeze pad of uniform thickness, choosing the diagonal sides of elements nearly perpendicular to the pressure gradient direction gives an error in the calculated load carrying capacity of over two times that obtained by aligning element diagonal sides approximately with the pressure gradient direction. For rotating bearings, varying the grid spacing in the circumferential direction directly as the film thickness and properly choosing diagonal alignment can significantly reduce computer time.