The work presented here demonstrates the capability of Gaussian Process (GP) regression for the prediction of aircraft structural loads based on recorded flight parameters. The objective of monitoring aircraft loads during operation is to develop a better understanding of aircraft usage and thus to provide the operator with an accurate estimate of the remaining useful life of components against their prescribed fatigue life. These loads are often difficult and expensive to measure and this motivates the use of advanced mathematical techniques to estimate them accurately based on other parameters that are typically measured during flight. Gaussian Process regression is a powerful Bayesian machine learning tool whereby predictions and their distributions can be obtained without having to specify a particular model/functional form. Data collected from a military trainer aircraft is used to demonstrate how the mapping of measured strains to basic flight parameters such as airspeed, accelerations, and control surface deflections can be performed using GP regression. It is also shown how these results can be applied in an aircraft usage monitoring context. The GP predictions for strain are compared to the actual measurements for 101 flights, and the results are presented in terms of fatigue life, correlation, and mean-squared error. The results are encouraging, with errors in fatigue life in the range of 5% to 30% in the worst cases.