In this study, an analytical solution is presented for elastic-plastic pure bending of a linear kinematic hardening curved beam with rectangular cross section both in monotonic loading and unloading. Compared to exact plane plasticity solution (already reported in the literature in loading) which needs solution of a system of equations, the proposed method is based on the hyperbolic strain distribution on the cross section which yields a simple approximate solution. To this end, we employ Winkler's theory, and assume plane cross sections remain plane after loading proved by the exact elasticity and plasticity solutions for pure bending of curved beams with rectangular cross section. At the loading stages, the equations required to obtain the location of the neutral axis, the location of inner and outer elastic-plastic borders, the stress distribution on the cross section, and moment-curvature relation are presented. At the unloading stages, taking reverse yielding of some fibers into account, the stress distribution on the cross section after unloading and final curvature of the curved beam are also determined. Finally, the results are validated and compared with the exact plane plasticity and finite element results. © 2018 Elsevier Ltd