A method has been developed for calculating the interaction pressure between a half-space consisting of a uniform material and a half-space with a spatially periodic material distribution based on the Lennard-Jones potential. The periodic material distribution is two dimensional in the x- and y-directions. The periodically distributed material property function is expanded as a complex Fourier series. The interaction pressures consist of both the attractive and repulsive pressures. The interaction pressures for a distribution of two materials were then calculated as a typical example of a periodic material distribution. The basic characteristics of the interaction pressure are clarified.