The rigid-plastic finite element method which is based on the upper bound theorem in plasticity is applied to the study of deformation behaviour of inhomogeneous materials with inclusions. The axisymmetric inclusion problem is studied in the present paper. The penalty method and the Newton-Raphson's repeated calculation is adopted to minimize a functional and to obtain the solution. Characteristics of the deformation behaviour of inhogeneous material are discussed based on the calculated results. The effects of the aspect ratio, the volume fraction and the yield stress ratio of inclusions on the deformation behaviour are investigated. The mean yield stress of inhomogeneous material is estimated based on microscopic deformation in the inclusion and the matrix.