ONE OF IMAGING MODALITIES IN MEDICINE IS ULTRASOUND SYSTEM, THE PRINCIPLE ULTRASOUND IMAGES ARE TWO-DIMENSIONAL, AND HOWEVER THREE-DIMENSIONAL IMAGES OFFER BETTER OBSERVATION AND INTERPRETATION. TO CREATE ULTRASOUND THREE-DIMENSIONAL IMAGES, SPECIAL TRANSDUCERS WITH TWO-DIMENSIONAL ARRAYS ARE USED. THESE TRANSDUCERS CONSIST OF PIEZOELECTRIC ELEMENTS ARRANGED TWO DIMENSIONALLY, SINCE THE CONSTRUCTION OF SUCH TWO DIMENSIONAL TRANSDUCERS ARE COMPLEX; SIMULATION OF THE TRANSDUCERS IS AN APPROPRIATE WAY TO OPTIMIZE THEIR BEAM PATTERN FOR A PARTICULAR APPLICATION. FOR THIS REASON IN THIS RESEARCH THE EQUATIONS OF BEAM PATTERN ARE DERIVED AND THEN SIMULATED, THE KEY PARAMETERS EFFECTIVELY THE BEAM PATTERN CAN BE ALTERED BY USER TO OPTIMIZE BEAM PATTERN FOR A PARTICULAR APPLICATION. THE RESULT OF THE OPTIMIZATION IS SHOWN GRAPHICALLY AND CAN BE ANALYZED EFFICIENTLY. THIS RESEARCH CAN BE USED AS AN APPROPRIATE TOOL FOR THE DESIGN OF ONE-DIMENSIONAL OR TWO DIMENSIONAL ARRAY TRANSDUCERS.