In current study natural convection flow of second grade fluid in an oscillating infinite vertical cylinder is investigated. The dimensionless governing equations for temperature and velocity are obtained by introducing the non-dimensional variables. Exact solutions for temperature and velocity field are computed by means of integral transformation. Solutions for cosine and sine oscillations of velocity field are introduced in the form of transient and post-transient arrangements. A special case for Newtonian fluid is obtained from general results and transients solutions are computed in terms of tables. In the end, the impact of dimensionless numbers (Grashof and Prandtl numbers) at different values of time is presented in graphical form and found that velocity for Newtonian fluid has greater values than the second grade fluid. Furthermore, there are some comparisons of calculated solutions with existing solutions in literature.