  We propose a two-sublattice proton ordering model for the
quasione-dimensional CsH$_2$PO$_4$ ferroelectric with hydrogen bonds, which
takes into account linear on lattice strains $u_1$, $u_2$, $u_3$ and $u_5$
contribution to the energy of proton subsystem. The model also takes into
account the dependence of effective dipole moments of pseudospins on the order
parameters, which enables one to agree the effective dipole moments in
paraelectric and ferroelectric phases. Within this model in two-particle
cluster approximation on short-range interactions and in the mean field
approximation on long-range interactions, there is investigated the behaviour
of spontaneous polarization, longitudinal dielectric permittivity and molar
heat capacity under the action of hydrostatic pressure and longitudinal
electric field. The phase transition into antiferroelectric phase under high
pressures is explained. The character of smearing of the
paraelectric-ferroelectric phase transition as well as suppression of the
antiferroelectric phase at the presence of electric field is studied.
