The available transfer capability (ATC) between two buses determines the maximum additional power that can be transmitted in an interchange schedule between the specified buses. The ATC changes probabilistically due to the stochastic nature of power system equipment availability and power system loads. An evaluation of the stochastic behavior of the ATC is important for an assessment of the ATC. The ATC is determined by power flow study subject to transmission system limits. These phenomena are nonlinear in behavior. Linearization can be used to estimate line flows in a power flow study model. This paper proposes a method of finding the stochastic ATC using a linear Gaussian transformation of line power flow statistical moments into ATC statistical moments. The probability density function of the ATC is approximated using a Gram Charlier type A series. The evaluation is illustrated for the IEEE 118 bus system. The results are an approximate evaluation of the probability density of the ATC; and its expectation.