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Memristor is claimed as a passive two terminal fundamental circuit element in 1971 and declared to be physically fabricated in 2008. The memristor can provide new features in analog circuit design thanks to its properties which cannot be mimicked by a resistor, a capacitor and an inductor. It is believed that in future it can be used in analog applications such as programmable amplifiers, oscillators, filters and chaotic sources. In this paper, detailed simulations of a low-pass filter and a high-pass filter with memristor are done using a piece-wise linear hypothetical memristor characteristic for sinusoidal input. The memristive switching issue in these filters is analyzed. Also the total harmonic distortions of the memristor based filters are inspected as a function of charge and the input signal frequency using simulations.