Fairness in multiple-path optimal routing algorithms in virtual circuit data networks is investigated. Fairness measures are developed to evaluate optimal routings. Several objective functions are considered to be possible replacements of the average packet delay objective function that is widely used in optimal routing algorithms, and evaluated for various network and traffic configurations. A numerical study using the fairness measures developed shows that the objective function which is in the integral form of the average packet delay achieves perfect fairness while sacrificing only a nominal increase in the average packet delay. The numerical study also confirms the conjecture by D.P. Bertsekas and R.G. Gallager (1987) that the form of objective function does not affect the average packet delay in any significant way.>