The dynamical evolution of buoyancy-driven geological systems is mainly influenced by two physical parameters: density and equivalent viscosity. Salt structures are an appropriate geological representation of these systems. Important variations of these parameters are directly related to changes in mass, and thus the internal structures themselves and their changes in time become significant parameters. In order to decipher these structures in nature by means of experiments it is therefore necessary to extend model calculations on intrusion processes to multilayer systems. A two-dimensional finite element program has been developed to simulate the rise of individual diapirs through multi-layered overburdens exhibiting Newtonian-viscous rheologies. This program includes the following features: arbitrarily shaped interfaces between different fluid boundaries, layers of finite thickness and subsidence of the model within the model-frame as well as time- and depth-dependent material properties. This paper is concerned with single diapirs intruding upbuilt dounbuilding, and differential loading of gravitationally unstable distributions of mass. Variable density and viscosity of the overburden with depth control the shape and ascent rates of diapiric bodies. The subsidence history of ''salt structures'' dominates the development of maximum horizontal pressure gradients with time and thus the ascend histories of diapirs.