According to wave theory, when a wavefront strikes a metal surface, the free electrons at the surface absorb the radiant energy continuously. Also greater is the intensity, greater are the amplitudes and energies of the wave' Hence, higher intensity wave should liberate photoelectrons with greater kinetic energies.

A light wave of sufficient intensity should be able to eject electrons, whatever may be the frequency and each electron intercepts an insignificantly some amount of energy and therefore should require a finite time to escape from the metal surface. 

Where as, according to photoelectric effect, maximum kinetic energy of emitted photoelectrons is independent of the intensity of incident radiation. High energy, (higher frequency) radiations of very low intensity can emit photoelechons, whereas higher intensity but low energy (below threshold energy) can't Wave theory fails to explain the existence of threshold energy. Also, emission of photoelectrons is instantaneous Process (within 10^-9 sec).