In this technical report we describe the method of solution to a variety of two-dimensional problems involving semi-immersed cylinders of rectangular cross-section piercing the free surface of a fluid of constant finite depth h. The aim is to be able to calculate the various components of added mass and radiation damping coefficients which can be used to characterise the two-dimensional time-harmonic oscillations of a cylinder in waves. The problems of a single cylinder making forced oscillations in sway, heave and roll in fluid of unbounded horizontal extent are considered first. Similar calculations are then made for a cylinder in forced motion placed next to a vertical wall.