The paper presents a method for simulating pulsed pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers. The approach is based on the Topholme–Stepanishen method, which provides an exact solution for a transducer modeled as a planar piston vibrating uniformly in an infinite rigid, planar baffle. The method can handle both continuous wave and pulse-echo cases. The field is calculated by dividing the transducer surface into small rectangles and summing their responses, with a fast calculation achieved using the far-field approximation. The accuracy and computational times are demonstrated through examples, showing that the method is accurate and efficient. The paper also discusses the influence of apodization and phasing on the transducer elements, and provides guidelines for choosing the number of elements and computing times. The method is validated through comparisons with analytic solutions and measurements, demonstrating good agreement. The main limitation of the approach is the use of the far-field approximation, which can be improved in future work to enhance accuracy while maintaining computational efficiency.The paper presents a method for simulating pulsed pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers. The approach is based on the Topholme–Stepanishen method, which provides an exact solution for a transducer modeled as a planar piston vibrating uniformly in an infinite rigid, planar baffle. The method can handle both continuous wave and pulse-echo cases. The field is calculated by dividing the transducer surface into small rectangles and summing their responses, with a fast calculation achieved using the far-field approximation. The accuracy and computational times are demonstrated through examples, showing that the method is accurate and efficient. The paper also discusses the influence of apodization and phasing on the transducer elements, and provides guidelines for choosing the number of elements and computing times. The method is validated through comparisons with analytic solutions and measurements, demonstrating good agreement. The main limitation of the approach is the use of the far-field approximation, which can be improved in future work to enhance accuracy while maintaining computational efficiency.