The common use of pressure vessels (PVs) and pipelines and the high cost of their failure or overdesign in the oil and gas industry makes predicting their burst pressure critical. However, experimental tests of burst pressure are expensive and finite element analysis (FEA) is time consuming. Artificial neural networks (ANNs) hold the promise of rapid prediction of burst pressure for a wide range of PV materials and geometries, including pipelines with defects such as corrosion. This paper demonstrates ANNs designed and trained to accurately predict the burst pressure of both thick and thin-walled PVs for various strain hardening carbon steels. To accomplish this, we trained single and double hidden layer ANNs on experimental data, augmented with FEA, data of predicted burst pressure to create a larger database. A statistical study of hundreds of models exploring the key hyperparameters provided statistically optimal hyperparameters, resulting in highly accurate ANNs. The results, two ANNs with comparably low prediction error across geometries ranging from 3 < Do/t < 120, demonstrate the first use of ANNs to address both thick and thin-walled PV burst pressure within a single network. This is an important step towards designing ANNs for predicting the burst pressure of PVs and pipelines with defects.