The problem of water wave propagation over a rectangular submarine trench in the presence of a thin vertical partially immersed barrier for its three different positions are investigated here assuming linear theory. For each position of the barrier, the problem is reduced to solving three weakly singular integral equations of first kind involving horizontal component of velocity above the two edges of the trench and below the barrier. The integral equations are solved employing Galerkin approximation in terms of simple polynomials multiplied by appropriate weight functions whose forms are dictated by the edge conditions at the corners of the trench and at the submerged end of the barrier. The numerical estimates for reflection and transmission coefficients are depicted graphically against the wave number for different lengths and positions of the barrier. © 2021 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.