The interaction stresses acting between a half-space consisting of a uniform material and a half-space with one-dimensional material distribution in the in-plane direction have been derived. Two patterns of material distribution are considered here, i.e., a periodic distribution of materials (Pattern 1) and a distribution of two materials with a single interface (Pattern 2). The interaction stresses for Pattern 1 was derived by using a Fourier series, while the interaction stresses for Pattern 2 was derived as elementary functions. The basic characteristics of these interaction stresses were clarified.