An efficient nonequilibrium Monte Carlo method using the Bond fluctuation model is used to simulate uniaxial and planar extension of dilute polymer solutions. The time scale is obtained from the stress relaxation of a fully stretched chain and can be related to the longest relaxation time of a real molecule, while the length scale is taken to be the statistical Kuhn segment length. The method leads to tau(1) similar to N-2.16 and D similar to N-1.02 for a freely draining chain with an excluded volume constraint, where tau(1), N, and D are the longest relaxation time, chain length, and diffusion coefficient, respectively. The finite extensibility of the bond causes extension thinning following the coil-stretch transition. The Monte Carlo predictions for the transient extension of isolated DNA molecules in a planar extensional flow agree reasonably well with published experimental measurements and Brownian dynamics simulations. "Molecular individualism" is observed in the unraveling of the polymer chain. (C) 2004 The Society of Rheology.