Abstract: The nonlinear pulsed acoustic pressure field from a focused square aperture is considered. Experimental measurements in water of a 4D sound field radiated from a 2.8 MHz focused square transducer of a 20 mm side and a 80 mm focal distance for excitation level producing an average acoustic pressure P₀ = 0.14 MPa at its surface are presented. The obtained results are compared with the numerical calculation results for the same boundary conditions. The novel, free from paraxial approximation and computationally efficient numerical algorithm was used to simulate the 4D nonlinear pulsed pressure field from the nonaxisymmetric acoustic source. Our theoretical model was based on the Time-Averaged Pressure Envelope (TAPE) method recently developed that enable to represent the propagated pulsed disturbance as a superposition of sinusoidal wavelets with carrier frequencies being the harmonics of the initial tone burst and with envelopes determined by the TAPE method. The novel approach to the solution of the nonlinear wave equation enabled to simulate full 4D nonlinear field for given boundary conditions in a dozen or so minutes utilizing the computational power of the standard PC.