Direct observations of long flexible polymers in elongational flow show a coil to stretch transition (CST) and hysteresis in this transition. In this article, solvent effects on the hysteresis of CST were examined using Brownian dynamics simulations of a dumbbell model with conformation dependent drag. A spring force relation that is able to capture the effects of solvent quality was used. Two methods of increasing the solvent quality were analyzed: (1) by increasing the number of Kuhn steps (N-K) and keeping the excluded volume parameter (v/l(3)) constant, and (2) by increasing v/l(3) and keeping N-K constant. In the first case, the width of the hysteresis (ratio of upturn to downturn strain rates) increased with increase in N-K. In the second case, the width of hysteresis decreased with increase in v/l(3). This implies that molecules such as ss-DNA, which have v/l(3) approximate to 1 in good solvents, will have less hysteresis than a molecule with the same N-K in a Theta solvent.