This paper presents a new formalism for simulating highly deformable bodies with a particle system. Smoothed particles represent sample points that enable the approximation of the values and derivatives of local physical quantities inside a medium. They ensure valid and stable simulation of state equations that describe the physical behavior of the material. We extend the initial formalism, first introduced for simulating cosmological fluids, to the animation of inelastic bodies with a wide range of stiffness and viscosity. We show that the smoothed particles paradigm leads to a coherent definition of the object's surface as an iso-surface of the mass density function. Implementation issues are discussed, including an efficient integration scheme using individually adapted time steps to integrate particle motion. Animation requires a linear complexity in the number of particles, offering reasonable time and memory use.