  Integral balance solution employing entire domain approximation and the
penetration dept concept to the Stokes' first problem of a viscoelastic
generalized second grade fluid has been developed. The solution has been
performed by a parabolic profile with an unspecified exponent allowing
optimization through minimization of the norm over the domain of the
penetration depth. The closed form solution explicitly defines two
dimensionless similarity variables and, responsible for the viscous and the
elastic responses of the fluid to the step jump at the boundary. The solution
was developed with three forms of the governing equation through its two
dimensional forms (the main solution and example 1) and the dimensionless
version showing various sides of the flow field and how the dimensionless
groups control it: mainly the effect of the Deborah number. Numerical
simulations demonstrating the effect of the various operating parameter and
fluid properties on the developed flow filed have been performed.
