The steady-state properties of flexible polymer chains in solutions undergoing elongational flow have been studied using Brownian dynamics simulation. The coil-stretch transition is observed when the elongational rate, (epsilon) over dot exceeds a certain critical value (epsilon) over dot(c). In this work, we describe in detail the simulation procedure and how to extract polymer dimensions, solution viscosity, and birefringence from the trajectories. Preliminary simulations involving no hydrodynamic interaction (HI) are used to check the simulation procedures by comparing their results with theoretical predictions for such an (unphysical) case. Afterwards, simulations with fluctuating nonaveraged HI are carried out to provide results comparable with experiments. After simulations with and without intramolecular potential, we arrive at a most important conclusion: the chain length dependence of (epsilon) over dot(c) is the same in theta conditions as in good solvent conditions. Combining (epsilon) over dot(c) with other solution properties such as the longest relaxation time, the intrinsic viscosity, and the radius of gyration, dimensionless compound quantities can be formulated. From our simulation results, we obtain numerical values for such quantities, which include the HI effect, and which are therefore useful for analyzing experimental data.