A method for the simulation of pulsed pressure fields from arbitrarily shaped, apodized and excited ultrasound transducers is suggested. It relies on the Tupholme-Stepanishen method for calculating pulsed pressure fields, and can also handle the continuous wave and pulse-echo case. The field is calculated by dividing the surface into small rectangles and then summing their response. A fast calculation is obtained by using the farfield approximation. Examples of the accuracy of the approach and actual calculation times are given.