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The algorithm developed by Moses in the late 70’s continues to be the most popular algorithm in commercial Bridge Weigh-In-Motion (B-WIM) systems. Moses’ approach consists of solving a set of simultaneous equations to calculate individual axle forces. Studies have shown, in general, good accuracy for estimating gross vehicle weights; however accuracy decreases for individual axle weights. It has been found that the equations are ill-conditioned, particularly for closely spaced axles and on bridges with longer spans. This paper proposes to apply the method of Tikhonov regularization to the original Moses equations to reduce some of the inaccuracies inherent to the algorithm for axle weights. The optimal regularization parameter is calculated using the L-curve criterion. The new regularized solution to the BWIM equations is tested using measured data obtained from the passage of a vehicle over a bridge and compared to the conventional (Moses) B-WIM solution.