The issues of stability of suspended crane booms of constant and variable cross-sections with their rigid and elastic embedding in the base, as well as the stability of the boom system - tower crane column and the boom system - geese of a self-propelled boom crane are considered. An overview and analysis of methods for solving problems to determine stability using simplified calculation schemes is given. Graphoanalytical method for calculation of compressed crane booms, dynamic method for determination of critical loads on metal structures of cranes are considered. The results of experimental studies of boom models for stability are presented.