In this investigation, the 3D stress field of a single cylindrical fiber, which is embedded into a plate matrix, is examined. The composite body is subjected to an axial loading and both perfect imperfect bonding conditions at the interface are considered. The analysis, which is based on analytical considerations, reveals the load transfer characteristics from the fiber to the matrix and vice versa. Numerical results for the displacement and stress fields are given and shown to be sensitive to the diameter to thickness ratio, the respective material properties and the applied load ratio between the fiber and the matrix. Comparisons with available experimental data shows a very good agreement.