  In this paper we discuss mechanical systems with inequality constraints. We
demonstrate how such constraints can be taken into account by proper
modification of the action which describes the original unconstrained dynamics.
To illustrate this approach we consider a harmonic oscillator in the model with
limiting velocity. We compare the behavior of such an oscillator with the
behavior of a relativistic oscillator and demonstrated that when an amplitude
of the oscillator is large the properties of both type of oscillators are quite
similar. We also briefly discuss inequality constraints which contain higher
derivatives.
