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We propose a new type of open resonator, a resonator with focused travelling wave pulses. Our first paper about such resonators was published in 1996 [1]. This non-sinusoidal travelling wave is of the form of a radio pulse, compressed in space and time. The open resonator is formed by means of two identical confocal parabolic mirrors (Fig. 1). A use of spherical mirrors is also possible, though the result would be somewhat worse. A mathematical model for computing near electromagnetic fields inside the resonator is developed. This model uses a new representation of mirrors as antenna arrays with special elements performance. Model is based on the matrix theory of antenna arrays with arbitrary geometry, published earlier [2]. The algorithm is realized on personal computer with opportunities of numerical evaluation of characteristics of the focal region, where the total electromagnetic field represents a wide-angle short-pulse wavebeam. The electromagnetic field in focal region is approximately in the form of travelling electromagnetic wave.