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The ability to numerically determine the received signal in an ultrasound pulse-echo system is very important for the development of new ultrasound applications, such as tissue characterization, complex object recognition, and identification of surface topology. The output signal from an ultrasound pulse-echo system depends on the transducer geometry, reflector shape, location and orientation, among others, therefore, only by numerical modeling can the output signal for a given measurement configuration be predicted. This thesis concerns about the numerical modeling and optimal design of annular array based ultrasound pulse-echo system for object recognition. Two numerical modeling methods have been implemented and evaluated for calculating received signal in a pulse-echo system. One is the simple, but computationally demanding Huygens Method and the other one is the computationally more efficient Diffraction Response for Extended Area Method (DREAM). The modeling concept is further extended for pulse-echo system with planar annular array. The optimal design of the ultrasound pulse-echo system is based on annular array transducer that gives us the flexibility to create a wide variety of insonifying fields and receiver characteristics. As the first step towards solving the optimization problem for general conditions, the problem of optimally identifying two specific reflectors is investigated. Two optimization methods, the straightforward, but computationally intensive Global Search Method and the efficient Waveform Alignment Method, have been investigated and compared.