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The emerging field of communications has increased the demand of electronically tunable reflectarray antennas. Substrate material properties play an important role in the design of reflectarray antennas. Variable permittivity materials such as liquid crystals and ferroelectrics have received great deal of attention due to their non-linear material properties. A comparative analysis between the properties of liquid crystals and ferroelectrics for tunable reflectarray antenna design has been carried out by using Finite Integral Method (FIM). A thorough investigation based on reflectarray design analysis and tunable bias voltages of different non-linear materials is provided. It has been shown that due to higher dielectric permittivity values of non-linear materials, ferroelectrics require higher bias voltages for electronic tunability, as compared to liquid crystal materials. Barium strontium titanate (BST) with a dielectric permittivity ranging from 300 to 360 has been used as a ferroelectric substrate material to design a rectangular patch reflectarray which offers a frequency tunability of 3 GHz. The results show that ferroelectrics are only applicable for high frequency reflectarray operation due to materials' higher permittivity values. Furthermore a rectangular patch reflectarray antenna printed on 1 mm thick different liquid crystal materials has also been designed based on FIM. It has been shown that as the dielectric anisotropy of substrate material increases from 0.17 to 0.45, the frequency tunablity and dynamic phase range of reflectarray antenna also increase from 372 MHz to 795 MHz and 90° to 160°, respectively. [ABSTRACT FROM AUTHOR]