We describe a full-chain stochastic tube model for entangled melts and solutions of linear polymers. The model incorporates two forces that result from chain confinement: a tensile force along the chain that prevents chain collapse and a transverse force that keeps the chain within the virtual tube. The model tracks conjugate constraint pairs and utilizes a consistent approach to constraint release and renewal. Chain loops within the tube are permitted. A single time-scaling adjustable parameter is required. Model predictions are compared with published transient and steady-state data on two entangled polystyrene solutions. (c) 2006 The Society of Rheology.