Self-assembling systems confined in slit-like pores of a width L are studied. We focus on phase transitions between uniform and ordered periodic phases. As shown by previous experimental and theoretical studies, the periodic phases respond elastically to the applied stress when the size lambda of the unit cell is much larger than the size of molecules. For such phases a simple modification of the Kelvin equation for the phase coexistence in a slit is derived. The shift of the phase transition in confinement is given by two terms. The first term is the standard Kelvin equation, and the second one depends on the elastic modulus of the periodic phase. The modified Kelvin equation (MKE) is verified by explicit calculations in a lattice model for oil-water-surfactant mixtures. We show that the two terms can be comparable even for L similar to 10 lambda. While for L >5 lambda the MKE is obeyed very well in our model, for narrow slits we find significant deviations between actual transitions and the MKE, associated with an inelastic behavior of the periodic phase for L <5 lambda. We also show that in self-assembling systems a phase which in bulk is not stable for any thermodynamical state (except for a line of muliphase points) can become stable in a slit with particular external surfaces.