We use Brownian dynamics simulation to study coil-stretch transition of macromolecules in solution. Into a simple elongational how field, we introduce freely jointed bead-rod chain model molecules in their coiled and stretched states, and follow the conformational changes. We find good agreement of our simulation results with the available theoretical predictions for low and high strain rates ((epsilon) over dot. At the intermediate elongation rates (near the onset of coil-stretch transition) of the flow field, we find that the residence time required for stretching of an initially coiled chain can be extremely large as compared to predicted (1 + ln(root N))(epsilon) over dot(-1), especially for the non-free-draining case, Hence, the chain conformation is dependent on the initial state of the chain molecule for residence time as long as 100(epsilon) over dot(-1). Thus, hysteresis is predicted when chain residence time in such an elongational flow field is limited, as in practical situations. Further, at such intermediate (epsilon) over dot, the chain molecule is seen to undergo Brownian fluctuation induced jumps between a randomly coiled state and another partially stretched state. This suggests the existence of more than one equilibrium conformation that is unstable to Brownian fluctuations.