The paper presents the developed algorithm which implements the indirect variational boundary element method (IVBEM) for computation of the free-field acoustic radiation characteristics of vibrating rectangle-shaped plate structures with arbitrary boundary conditions. In order to significantly reduce the computational time and cost, the algorithm takes advantage of simple geometry of the considered problem and symmetries between the elements. The procedure of determining the distribution of acoustic pressure is illustrated on the example of thin, rectangular plate with a part of one edge clamped and all other edges free. The eigenfrequencies and the corresponding vibrational mode shapes of the plate are computed using the finite element method (FEM). The results of the numerical simulations are compared to the results of the experiments carried out in an anechoic chamber, proving good agreement between the predictions and the observations. The reliability of simulations and high computational efficiency make the developed algorithm a useful tool in analysis of the acoustic radiation characteristics of vibrating plate structures.