Numerical method for detection of unstable periodic orbits on attractors of nonlinear dynamical systems is proposed. This method requires the similar techniques as the data assimilation does. This fact facilitates its implementation for geophysical models. Some low-period orbits of the Lorenz model have been calculated explicitely. The orbits encoding and application of symbolic dynamics is used to classify and identify the detected orbits and find the whole set of fundamental cycles. Application of the cycle expansion theory to the fundamental cycles set allows to approximate some attractor characteristics difficult to calculate directly.