The objective of the paper is to provide a suitable analytical approach to describe the behaviour of a square miniaturised (MEMS) receiving transducer made up of a square membrane having the same dimensions as the external dimensions of the transducer itself, loaded by both a thin square small sized fluid-gap and a peripheral cavity connected together and set rear the membrane. This device departs from the other previous square devices in that the peripheral cavity is rear the membrane at the periphery of the backing plate (backing electrode). This architecture (derived from the circular one suggested previously) enables to optimize the sensitivity of the transducer while retaining both a cartesian geometry and the smallest dimensions possible (surface area and thickness). The analytical approach accounting for the effects of the interior geometrical discontinuity on the displacement field of the membrane used here to describe such square transducers (electrostatic or piezoelectric) departs from previous ones in that it avoids multi-modal analysis which exhibits procedural difficulties due to the coupling of Dirichlet-like (membrane) and Neumann-like (fluid) eigenfunctions (emphasized here by presence of the geometrical discontinuity in the fluid-filled part of the device). Additionally, an approximate analytical solution appropriate to express the displacement field of the membrane and to estimate the sensitivity with a good accuracy in the lower frequency range is presented. FEM solutions are provided, against which the analytical results have been tested.