Conditions of stability of the magnetization curling mode in fine spherical and cylindrical particles and of the magnetization helicoid structure in fine cylindrical particles are derived, and magnetization reversal processes in such particles are considered. The application of Ritz's method for solving the variational problem of finding the local magnetization vectors in the volume of a particle provides a convenient way of finding the conditions mentioned above. It has been shown that the magnetization curling mode in a spherical fine particle with radius larger than a critical one is stable in a well-determined interval of the external magnetic field, provided the magnetocrystalline anisotropy constant is less than a certain value K0. In such a case the hysteresis loop of a spherical particle measured in an easy direction is no longer rectangular. The magnetization curling and helicoid modes are both unstable in fine cylindrical particles with positive or zero values of the magnetocrystalline anisotropy constant. The hysteresis loop of such particles magnetized along the axis of rotation is rectangular.