Abstract: The two dimensional equations of motions for the slowly flowing and heat transfer in second grade fluid are written in Cartesian coordinates neglecting the inertial terms. When the inertia terms are simply omitted from the equations of motions the resulting solutions are valid approximately for Re<<1. This fact can also be deduced from the dimensionless form of the momentum and energy equations. By employing Lie group analysis, the symmetries of the equations are calculated. The Lie algebra consists of four finite parameter and one infinite parameter Lie group transformations, one being the scaling symmetry and the others being translations. Two different types of solutions are found using the symmetries. Using translations in x and y coordinates, an exponential type of exact solution is presented. For the scaling symmetry, the outcoming ordinary differential equations are more involved and only a series type of approximate solution is presented. Finally, some boundary value problems are discussed.