It is useful to have an efficient method to determine the sound field in a room produced by a source that is not omnidirectional. A method is thus developed for simulating a “higher order” source with an arbitrary directional pattern in a reverberant room. Several types of directional sources are subsumed by the higher order source, including an arbitrarily vibrating cylinder and an array of vertical line sources arranged on a cylinder. The sound field is calculated by extending the image-source method. For simplicity the sound is modelled in 2-D where sources are either tall or have an infinite vertical extent. A modal expansion of the sound field is used, which reduces the computation of calculating the sound field over a large number of points. The method is particularly suited to array signal processing where the sound field is sampled at multiple points. Efficient algorithms are presented for simulating both circularly-shaped regions absent of sound sources and the entire room.