Abstract <p>We study a problem that simulates small deformations of a string with localized singularities in the form of elastic supports and concentrated forces at an arbitrary number of points (at most countable). It is assumed that the left end of the string is rigidly fixed and the right end is inside a vertical displacement limiter. Depending on the external force applied, the right end will either remain free or reach the limiter boundary. This generates a nonlinear condition at the corresponding point, since the behavior of the solution is not known in advance. The problem under study is described in the form of a variational inequality, theorems of existence and uniqueness of the solution are proved, an algorithm for finding an approximate solution using an adaptation of the finite element method is developed, and an estimate of the deviation of the exact solution from the approximate one is obtained.</p>