We propose a two-sublattice proton ordering model for the quasi-one-dimensional CsH2PO4 ferroelectric with hydrogen bonds, which takes into account contributions to the energy of the proton subsystem that are linear in the lattice strains Ξ΅1, Ξ΅2, Ξ΅3, and Ξ΅5. The model also takes into account the dependence of the eective dipole moments of pseudospins on the order parameters, which enables us to coordinate the values of the eective dipole moments in the paraelectric and ferroelectric phases. Within this model in the two-particle cluster approximation for the short-range interactions and in the mean eld approximation for the long-range interactions, the behavior of spontaneous polarization, longitudinal dielectric permittivity, piezoelectric and elastic characteristics, and molar heat capacity under the inuence of uniaxial and hydrostatic pressure and a longitudinal electric eld are investigated.