<p>Water wave interaction with a partially immersed rectangular block of two different geometrical configurations in the presence of an infinite step-type bottom is studied here. It is formulated in terms of coupled first-kind integral equations involving horizontal components of velocity below the two corners of the block and above the step. The integral equations are solved by employing Galerkin approximation in terms of simple polynomials multiplied by an exponential decay function and appropriate weight functions whose forms are dictated by the edge conditions at the corner of the step and at the submerged ends of the block. The reflection and transmission coefficients and hydrodynamic forces are then computed and depicted graphically against the wave number. The numerical results are validated by comparing them with the existing results graphically. The present study is likely to be important in the design of a breakwater in the presence of an infinite step.</p>