Abstract: In this paper we use quintic non-polynomial
spline functions to develop numerical methods for approximation
to the solution of a system of fourth-order boundaryvalue
problems associated with obstacle, unilateral and contact
problems. The convergence analysis of the methods has been
discussed and shown that the given approximations are better
than collocation and finite difference methods. Numerical
examples are presented to illustrate the applications of these
methods, and to compare the computed results with other
known methods.