We present theoretical studies for the conformational behavior of isolated polymers under an external field in good solvents. We assume the monomers of the polymer chain are subject to a three-dimensional external field, which is modeled as a spherical harmonic potential, and monomers interact via hard-core repulsions. We begin with Monte Carlo simulations to investigate the effects of the external field. The chain conformation changes insignificantly if the external field is weak. When the strength of the external field is increased, the chain contracts drastically. A first-order perturbation theory (with ideal-chain reference system) is proposed, with the hard-core repulsion modeled as a perturbation. This approach yields good agreement with the simulations, but with the discrepancy between these two approaches becoming pronounced for strong external field. The perturbation theory makes the prediction that the size of a polymer chain contracts approximately one order of magnitude before collapsing to its globular conformation. Further, to account for behavior under strong fields, a theory of mean-field type is developed, which predicts [R-2] similar to (N/k)(2/5) (where k denotes field strength), consistent with the simulations. These studies are of importance in understanding supercoiled long chain DNA in a tiny cellular nucleus, and deformation of polymer materials under external fields. (C) 2001 American Institute of Physics.