A theoretical examination is made of the convection of a fluid with uniform internal heat sources in a plane horizontal layer in the presence of harmonic high-frequency vibration of arbitrary orientation. The solid boundaries of the layer are kept at identical temperatures. The linear problem of mechanical equilibrium stability is solved numerically. The stability limits, parameters and form of critical disturbances are determined. The non-linear finite-amplitude regimes of convection and heat transfer are investigated by the method of finite differences. The presence of stationary and wave (drifting) regimes is established and their characteristics are studied.