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The fast Fourier transform (FFT) technology has been introduced into the process of contact analyses. However, a problem may occur at the borders of the domain due to a periodic error involved. In order to obtain reasonable results, an expedient treatment requires a computational physical domain much larger than the target domain at the cost of calculation efficiency. This paper studies the source of the error and investigates the methods that can help avoid this error and improve the efficiency. Discrete convolution and FFT (DC-FFT) is first adopted instead of the method of continuous convolution and Fourier transform for the contact problems. A few approaches based on the DC-FFT method are presented and numerical results are compared.