<p>The problem of wave interaction due to an impermeable trench bottom in a two-layer fluid is studied here, under a uniform current, oriented either in the opposite direction or in the direction of the incident wave. Both fluids are of finite depth bounded above by an undisturbed free surface and are assumed to be inviscid and incompressible. Linearized potential theory is used to solve the two-dimensional boundary-value problem. Associated with the trench position, the fluid domain is divided into five sub-domains. A dispersion relation for frequency as a function of wave number and other parameters involved in this problem is derived. A new form of the energy–balance identity is developed. Also, from this dispersion relation, the phase and group velocity for both surface and internal modes are obtained and plotted graphically. The wave blocking occurrence due to the effect of the current is shown here for deep-water and shallow-water approximations. Solving this boundary-value problem, free surface elevation, and reflection, transmission coefficients for surface mode (SM) and internal mode (IM) are derived numerically. Our findings indicate that the Froude number can occur in the presence of a uniform current for both SM and IM. This study aims to understand the effect of current and different geometric parameters on the wave propagation characteristics in the presence of variable bottom bathymetry.</p>