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Analysis of large finite antenna arrays presents unique challenges that have hindered its further development. It is common practice to combine the relatively easy infinite-array solution with an array factor to obtain an approximation to the finite array problem. However, this approximate solution may become inaccurate because of the so-called edge effects. In such situations, it is considered helpful to investigate finite-by-infinite arrays as an intermediate step. It is desirable to develop a numerical simulation tool that is capable of fast and reliable characterization of the properties of a general finite-by-infinite array. This work can be viewed as an extension of our previous work on the higher-order finite element analysis of infinite arrays (Lou, Z. and Jin, J.M., Microwave Opt. Tech. Lett., vol.37, no.3, p.203-7, 2003; vol.38, no.4, p.259-63, 2003). The new analysis takes one row of elements in the finite direction as the unit cell. The unit cell region is discretized with tetrahedral elements and the field is expanded with higher-order basis functions. Radiation boundary conditions imposed on the array aperture are derived via two different formulations and they are shown numerically to be equivalent. A specialized brick element code, which utilizes the conjugate gradient-fast Fourier transform (CG-FFT) method for improved efficiency, is also developed. Numerical examples are presented to demonstrate the accuracy and efficiency of the two codes.