The evolution of non-compressional sedimentary basins can be modelled in many ways. A number of existing schemes rely on assuming mathematical relationships between such geodynamical parameters as subsidence and heating of a basin and the amount of presumably causative tectonic extension. The usual objective is to determine precisely the geological history of a sedimentary basin, and to predict the unknown parameters. Models inevitably simplify complex natural systems. Many models of basin formation rely on specific assumptions about the dynamics of the crust (pure-shear or simple-shear deformation, the Moho as a passive marker, uniform extension, absence of older weakness zones, certain metamorphic reactions at depth, etc.) and about the structure and geological history of the basin (purely conductive heat transfer, existence of an underlying rift, etc.). Such assumptions cannot always be tested in poorly-studied regions, and in some cases they contradict the available geological information. For simplification to be valid, the, geological system has to be understood in some detail before model parameters are chosen. Misleading results may be obtained if an inappropriate model is applied, or if its parameters are ill-constrained. Many different geodynamical processes may, contribute to basin evolution. In the North Sea region, for example, both mantle-plume activity and mobility of lower-crustal material are proposed to have occurred in Mesozoic and Cenozoic times. The Jurassic plume may have been influenced in part by ancient lithospheric structure. The preferred method in basin analysis is the multidisciplinary approach based on a broad range of data, of which quantitative modelling may or may not be a part. In the integrated basin analysis, geological information is used to constrain the interpretation of gravity, magnetic and seismic data, thus revealing the structure of the basin and helping infer its geological history. Combined with geochemical data, these results are a useful guide for hydrocarbons exploration.