An analytical formulation for the second virial coefficient is given for a spherically symmetric potential function of a simple form which has been called a realistic pair potential. This potential, given as an inverse relationship with rasa function of U, is capable of being much softer than a Lennard-Jones in the extreme of close approach. Differing forms of the result are given, including an expression by means of the generalized hypergeometric series. The result is also expressed in terms of the second virial coefficient for the (12, 6) potential.