Assuming a polynomial of the fourth degree to describe the velocity function, the momentum integral equation for a second-order fluid is used to develop differential equations describing the boundary-layer for second-order flow past external surfaces. Using the momentum integral equation and appropriate boundary conditions, results are tabulated for both plane and axisymmetric stagnation flows. The effect of the second-order viscosity terms on the boundary-layer parameters for problems of flow past a circular cylinder and flow past a sphere is discussed. An interesting result is found in the case of flow past a sphere; for certain values of the second-order viscosity terms, there is a reduction in the viscous drag from that of Newtonian flow.