Damage pattern predictions of open-hole laminates under different loading conditions are ubiquitous in the finite element modelling of composite structures. This work investigated the applicability of artificial neural networks for the fast and accurate generation of damage patterns for a composite plate with a cut-out under a variety of loading conditions. The purpose is to explore the neural networks as surrogate models capable of returning damage pattern predictions on par with a finite element model, but requiring less computational effort at run time. Data for training and evaluating these neural networks was generated through nonlinear finite element models. Different neural networks, such as a standard Feedforward Neural Network and a Hybrid Neural Network that combines a Feedforward Neural Network with a convolutional decoder, have been tested for this task. To quantify the resemblance between the predicted and actual outputs in terms of colours and contours, different performance metrics have been explored. The use of the Structural Similarity Index (SSIM), in addition to the standard Mean Square Error (MSE), was explored to improve the visual quality of outputs from the neural network. With an average test MSE of 0.0014, SSIM of 0.9814, and computational speedup factor of 34, the Hybrid Neural Network has been shown to accurately and efficiently predict the damage patterns of the open-hole laminate, thereby constituting a promising candidate for a surrogate model of open-hole composite panels.