The study is concerned with the problem of direct numerical simulation of nonlinear evolution of random wave fields and is aimed at establishing the range of applicability of the classical kinetic description as well as the underlying statistical hypotheses. The problem is more challenging than DNS of turbulence, since to address this problem the study should involve integration of basic equations of hydrodynamics for a very large number of interacting modes over very long time spans with very high accuracy. At present DNS of the basic equations with desired accuracy over the required time scales is impractical if not impossible. We assume weak nonlinearity of the wave field and develop an algorithm based upon integration of the integro-differential Zakharov equation. We apply it to a number of

”model” problems where the required accuracy of simulation can be ensured. The study is focussed on modelling of evolution of finite number localized wave packets. The ensemble averaged results are compared with the solutions of the kinetic equation for water waves. It is found that an effective way of modelling the packets is to ”construct” them out of small number of discrete harmonics. Within a certain range of parameters neither the size of the clusters nor the number and positions of the constituting harmonics affect the evolution of the statistical characteristics of the wave field. It is shown that the nearresonant interactions play the key role in the nonlinear evolution, while modelling of a wave field by any number of strictly resonant harmonics leads to a qualitatively inadequate description of the field evolution. We compared the DNS predictions based on employing clusters for a wide range of field configurations. When the standard kinetic description is applicable, then the DNS predictions coincide with the solutions of the kinetic equations with a good accuracy. Application of the cluster approach for modelling evolution of the continuous wave fields and general issues concerned with the DNS are also discussed.