  In this paper we consider the possibility to use numerical simulations for a
computer assisted analysis of integrability of dynamical systems. We formulate
a rather general method of recovering the obstruction to integrability for the
systems with a small number of degrees of freedom. We generalize this method
using the results of KAM theory and stochastic approaches to the families of
parameter depending systems. This permits the localization of possible
integrability regions in the parameter space. We give some examples of
application of this approach to dynamical systems having mechanical origin.
