The ultrasonic field generated by a Micro Intereferometric Acoustic Lens used for high precision Rayleigh wave velocity measurements is modeled by the recently developed mesh-free technique called Distributed Point Source Method (DPSM). The field generated by the three individual ultrasonic transducer elements forming the micro intereferometric acoustic lens are computed and compared with experimental measurements. Qualitative agreement between the theoretical and experimental results is observed; both results show converging beams up to the focal point and then the beams diverge. However, some of the minute detailed features in the generated ultrasonic field could only be observed in the computed results. Effects of non-uniform surface of the transducer and its contribution to the non-uniform ultrasonic source strength are investigated to understand and optimize the acoustic lens for localized quantitative elastic property measurements.