In this article, results have been presented for the two-time correlation functions for a free and a harmonically confined Brownian particle in a simple shear flow. For a free Brownian particle, the motion along the direction of shear exhibit two distinct dynamics, with the mean-square-displacement being diffusive at short times while at late times scales as t 3 . In contrast the cross-correlation 〈 x(t)y(t) 〉 scales quadratically for all times. In the case of a harmonically trapped Brownian particle, the mean-square-displacement exhibits a plateau determined by the strength of the confinement and the shear. Further, the analysis is extended to a chain of Brownian particles interacting via a harmonic and a bending potential. Finally, the persistence probability is constructed from the two-time correlation functions.