The statistical-mechanical problem of chain pullout from an amorphous polymer under the influence of a constant force has been investigated. A simple microscopic model is proposed to describe the pullout process in both polymer glasses and elastomeric materials from a single point of view. A mean-field approximation for the interchain potential is used to account for the entanglements with the polymer network of the chain being pulled out. The chain mobility and the pullout rate were calculated as a function of pullout force, length of the chain, and other model parameters. In glassy polymers the pullout force was found to be almost rate independent at low pullout rates and linear in rate at high pullout rates. For polymer glasses the model also predicts the existence of some characteristic degree of polymerization N-e of the chain being pulled out, such that the pullout force scales as N for N much less than N-e but as N-3 for N much greater than N-e. In elastomeric materials the pullout force was found to have a nonlinear dependence on both chain length and rate of pullout.