Optimum design of structures for earthquake induced loading is achieved by a modified genetic algorithm (MGA). Some features of the simulated annealing (SA) are used to control various parameters of the genetic algorithm (GA). To reduce the computational work, a fast wavelet transform is used. The record is decomposed into two parts. One part contains the low frequency of the record, and the other contains the high frequency of the record. The low-frequency content is used for dynamic analysis. Then using a wavelet neural network, the dynamic responses of the structures are approximated. By such approximation, the dynamic analysis of the structure becomes unnecessary in the process of optimisation. The wavelet neural networks have been employed as a general approximation tool for the time history dynamic analysis. A number of structures are designed for optimal weight and the results are compared to those corresponding to the exact dynamic analysis.