The issue of static stiffness of tower crane is researched in current thesis to meet the need of modifying standard, GB/T 3811-83 "Design rules for cranes". Based on the mass data obtained from existing tower cranes and theoretical analysis, a reasonable static stiffness control value of tower crane is proposed. It has been accepted and recognized by the experts who are working for modifying above standard. Also, a theoretical approach of calculating static displacement of tower crane, which coincide with existing measurement method of static stiffness and a calculating approach of static displacement under working condition are developed.Because in the modifying draft of "Design rules for cranes", stiffness requirement for tower crane is only a reference value instead of a mandatory rule, a method is proposed to determine allowable static rigidity of tower crane. Based on the conception of two-stage fuzzy integrated judgment, the effect of some main fuzzy factor, such as, design and manufacturing level, working condition etc., on static stiffness of tower crane is considered. That will provide the feasible theory and method to new version of "Design rules for cranes", as well as practical cases.The dynamic rigidity of tower crane is the most important parameter, which affects dynamic characteristics of tower crane significantly. Usually, it is described in terms of natural frequencies. The dynamic models of tower crane structure system are built by means of lumped parameter method (LPM) and Finite Element Method (FEM) respectively. The low degree freedom (DOF) models of LPM include the four DOF, three DOF, two DOF and single DOF systems. Simplified formula is developed to calculate the structure natural frequencies for two and single DOF systems. It has been confirmed by practical cases that the accuracy of low DOF system and simplified formula meet the engineering design needs.A dynamic optimum design method is proposed. A dynamic optimum mathematical model of tower structure system is establishes to optimize the dynamic stiffness. The key mode frequency is determined via mode analysis and harmonic response analysis. Considering this frequency as objective function, sensitivity analysis has been done for all structure parameters to decide the dynamic optimum design variables. Dynamic optimum mathematic model is built with restraints of structure mass, static strength, static stiffness and dynamic displacement response amplitude. The result of analysis shows that after optimum, both static and dynamic characters are improved significantly, as well as lighten structure mass and decreasing manufacture cost effectively.Combining Finite Element Method, Orthogonal Experiment Method, BP Neural Networks and Genetic Algorithm, an approach is developed to perform dynamic optimum design for tower crane structure. FEM can be used to perform mode analysis, harmonic response, and sensitivity analysis to determine objective function of dynamic optimum, design variables and to calculate samples data needed by BP Neural Networks. Utilizing Orthogonal Experiment Method to design neural networks' samples can decrease sample size greatly and obtain the reasonable sample distribution. The dynamic analysis model is established by means of BP Neural Networks. It can replace traditional FEM model to realize fast re-analysis for vibration systems. Using genetic algorithm, the optimum result of Neural Networks model can be considered as the real optimum solution.