ESDU 97033 describes the most commonly used methods of prediction for structures and structures coupled to fluids. It provides guidelines for choosing an appropriate method for a given application. Various physical characteristics of the structural response are described that influence the selection of the most appropriate mathematical model to describe the complete system. The general principles of the methods for modelling the structure are described and their major advantages and limitations summarised. Methods covered are: global or local trial functions, the boundary element method, the finite element method, the dynamic stiffness method, modal interaction analysis, and statistical energy analysis. The mathematical approach for each method is outlined. Modelling the excitation is discussed. The advantages of choosing either a frequency or a time domain solution are also considered. The various options available appear on four decision trees that guide the user to select the most appropriate approach to model the complete system, and their use is illustrated by practical examples.