We investigate strong lensing by non-singular finite isothermal ellipsoids taking into account the influence of the matter along the line of sight and in the close lens vicinity. We compare three descriptions of light propagation: the full approach taking into account all matter inhomogeneities along the rays; the single plane approach, where we take into account the influence of the strong lens neighbours but neglect the foreground and background objects; and the single lens approach. In each case, we simulate many strong lensing configurations placing a point source at the same redshift but in different locations inside the region surrounded by caustics. We further analyse configurations of four or five images. For every simulated strong lensing configuration, we attempt to fit a simplified lens model using a single isothermal ellipsoid or a single isothermal ellipsoid with external shear. The single lens fits to configurations obtained in the full approach are rejected in majority of cases with 95 per cent significance. For configurations obtained in the single plane approach, the rejection rate is substantially lower. Also the inclusion of external shear in simplified modelling improves the chances of obtaining acceptable fits, but the problem is not solved completely. The quantitative estimates of the rates of rejection of simplified models depend on the required accuracy of the models, and we present few illustrative examples, which show that both matter close to the lens and matter along the rays do have important influence on lens modelling. We also estimate the typical value of the external shear and compare the fitted parameters of the simplified models with the parameters of the lenses used in the simulations.