A probabilistic neural network is used here to classify flaws in weldments from their ultrasonic scattering signatures. It is shown that such a network is both simple to construct and fast to train. Probabilistic nets are also shown to be able to exhibit the high performance of other neural networks, such as feed forward nets trained via back-propagation, while possessing important advantages of speed, explidtness of their architecture, and physical meaning of their outputs. Probabilistic nets are also demonstrated to have performance equal to common statistical approaches, such as the K-nearest neighbor method, while retaining their unique advantages.