Laser-induced breakdown spectroscopy (LIBS) is a rapid chemical analysis technique which has many applications in both science and industry.Traditional techniques for analyzing the spectra to predict elemental composition include partial least squares (PLS) and random forest regression, but these methods are limited in their scalability and performance.Recently, neural networks (NNs) have been applied to this task with the goal of achieving more accurate predictions. However, quantifying the predictive uncertainty of NNs is a challenge.In scientific domains, accurate estimates of predictive uncertainty are critical for evaluating model performance, particularly when trained models are applied to new data.In an effort to solve this problem, Bayesian Neural Networks (BNNs) introduce a probability distribution over model parameters to allow uncertainty to propagate through the network.Predictive queries can then be answered alongside various uncertainty measures. In this paper, we show that BNNs can provide good predictive performance on LIBS data while delivering additional insights on elemental compositions through well-calibrated uncertainty estimates.