Elastic two-layer curved composite beam with partial shear interaction is considered. It is assumed that each curved layer separately follows the Euler-Bernoulli hypothesis and the load slip relation for the flexible shear connection is a linear relationship. The curved composite beam at one of the end cross sections is fixed and the other end cross section is subjected by a concentrated radial load. Two cases are considered. In the first case the loaded end cross section is closed by a rigid plate and in the second case the radial load is applied immediately to it. The paper gives solutions for radial displacements, slips and stresses. The presented examples can be used as benchmark for the other types of solutions as given in this study.