The NA57 experiment has collected high statistics, high purity samples of K_S⁰ and Λ, ξ and Ω hyperons produced in Pb-Pb collisions at 158 A GeV/c. In this paper we present a study of the transverse mass spectra of these particles for a sample of events corresponding to the most central 53% of the inelastic Pb-Pb cross-section. We analyse the transverse mass distributions in the framework of the blast-wave model for the full sample and, for the first time at the SPS, as a function of the event centrality.