Abstract: A physically based model of an object is a mathematical representation of its behavior, which incorporates principles of Newtonian physics. Dynamic soil models are required in animations and realtime interactive simulations in which changes of natural terrain are involved. Analytic methods, based on soil properties and Newtonian physics, are presented in the paper to model soil slippage and soil manipulations. These methods can be used to calculate the evolution of a given soil configuration under the constraint of volume conservation and to simulate excavating activities such as digging, cutting, piling, carrying or dumping soil. Numerical algorithms with linear time and space complexities are also developed to meet the requirement of realtime computer simulation.