RBaCo4O7 (R = rare earth ion or Y) compositions belong to class of strongly frustrated antiferromagnets. Their crystal structure is build up of alternating Kagome and triangular cobalt lattices and represents a new type of geometrically frustrated topology. However, a first order structural phase transition whose critical temperature is a function of R releases the frustration and results in a long range magnetic order at low temperature. A suppression of the structural instability is, therefore, a necessary condition to study magnetic behavior of the highly frustrated phase. Analysis of the chemical pressure effect allowed us to suggest that application of an external pressure can be an effective way to preserve the frustration down to low temperatures. Thus, the main aim of the proposal is to study the pressure effect on structural behavior of the RBaCo4O7 compositions.