This paper aims to clarify the influence that initial perturbations have in controlling the buckling process. The questions are: how is the Biot-Ramberg dominant wavelength modified by the presence of finite initial perturbations? How is the shape of the resultant folds influenced by the initial geometry? In answering these questions we also revisit many of the results already embedded in the literature for viscous materials but contrast the behaviour of these materials with those of strongly pressure-dependent elastic-plastic materials; this paper represents the first time that the buckling behaviour of such materials has been reported. For layers with a series of initial small perturbations, the current results confirm that fold wavelength and growth rate are controlled by competence contrast (R). Wavelength selection also occurs in a layer involving perfectly-sinusoidal small perturbations, resulting in a dominant wavelength different from the input one. For layers with an isolated initial perturbation, both R and initial perturbation geometries influence buckling. If the width of the initial perturbation is smaller than a critical width related to R, significant growth of the initial perturbation is possible. When the width of the initial perturbation is larger than the critical width, the simple growth of the perturbation is possible only for early stages. It then splits into two or more secondary perturbations according to R. These perturbations can all grow into finite folds in elastic-viscous models, but only some of them can do so in elasticplastic models.