  Nonlinear dynamics of the free surface of an ideal incompressible
non-conducting fluid with high dielectric constant subjected by strong
horizontal electric field is simulated on the base of the method of conformal
transformations. It is demonstrated that interaction of counter-propagating
waves leads to formation of regions with steep wave front at the fluid surface;
angles of the boundary inclination tend to {\pi}/2, and the curvature of
surface extremely increases. A significant concentration of the energy of the
system occurs at these points. From the physical point of view, the appearance
of these singularities corresponds to formation of regions at the fluid surface
where pressure exerted by electric field undergoes a discontinuity and
dynamical pressure increases almost an order of magnitude.
