  In this work we study classical bouncing solutions in the context of $f({\sf
R},{\sf T})={\sf R}+h({\sf T})$ gravity in a flat {\sf FLRW} background using a
perfect fluid as the only matter content. Our investigation is based on
introducing an effective fluid through defining effective energy density and
pressure; we call this reformulation as the "effective picture". These
definitions have been already introduced to study the energy conditions in
$f({\sf R},{\sf T})$ gravity. We examine various models to which different
effective equations of state, corresponding to different $h({\sf T})$
functions, can be attributed. It is also discussed that one can link between an
assumed $f({\sf R},{\sf T})$ model in the effective picture and the theories
with generalized equation of state ({\sf EoS}). We obtain cosmological
scenarios exhibiting a nonsingular bounce before and after which the Universe
lives within a de-Sitter phase. We then proceed to find general solutions for
matter bounce and investigate their properties. We show that the properties of
bouncing solution in the effective picture of $f({\sf R},{\sf T})$ gravity are
as follows: for a specific form of the $f({\sf R,T})$ function, these solutions
are without any future singularities. Moreover, stability analysis of the
nonsingular solutions through matter density perturbations revealed that except
two of the models, the parameters of scalar-type perturbations for the other
ones have a slight transient fluctuation around the bounce point and damp to
zero or a finite value at late times. Hence these bouncing solutions are stable
against scalar-type perturbations. It is possible that all energy conditions be
respected by the real perfect fluid, however, the null and the strong energy
conditions can be violated by the effective fluid near the bounce event.
