<p>This paper explored a bouncing cosmology within the framework of <i>f</i>(<i>R</i>,&#xa0;<i>T</i>) modified gravity. We analyzed the dynamical behavior of the model, demonstrating the recovery of a flat FLRW space-time along with the necessary violation of the null energy condition. At the bouncing epoch, the geometric properties exhibit singular behavior. The occurrence of a bounce is strongly influenced by the parameters of the scale factor. Furthermore, the coupling parameter, which governs the matter-geometry interaction in <i>f</i>(<i>R</i>,&#xa0;<i>T</i>) gravity, plays a significant role in affecting the singularity of the equation of state parameter at the bounce. Finally, we evaluated the model stability using the ‘sound speed approach,’ providing insights into the system behavior during late-time evolution.</p>