This paper concerns the modeling of an eddy current damper with a finite conducting plate. In the eddy current damper a finite rectangular conducting plate is moving between cuboidal magnets. The first step of the modeling method is based on an infinite conducting plate. For this infinite conducting plate the eddy current density is derived using two different methods, the scalar potential method and the vector potential method. The finite boundaries of the conducting plate are included by means of the method of images in two dimensions and, therewith, completes the model. By applying the method of images, the accuracy of the models for calculating the damping coefficient is significantly improved. The assumption of an infinite conducting plate gives less than 15 % error for a conducting plate with at least twice the dimensions of the permanent magnet. Applying the method of images reduces the modeling error for a conducting plate with two times the permanent magnet dimensions to less than 3 % in respect to a finite element model. For verification of the semianalytical model, measurements are performed. For a variation of plate width, the presented semi-analytical model has less than 5 % discrepancy with respect to the measurements.