Many around the world are afflicted by facial palsy and paresis due to various causes. Prompt and reliable evaluation of such conditions is crucial in their effective treatments, potentially aiding in circumventing more serious underlying problems such as stroke. Facial palsy and paresis are commonly presented with abnormalities in a patient’s facial appearance such as symmetry. Computer vision-based automatic evaluation of facial palsy and paresis through analysis of facial shape and features has attracted research interest. In this paper, we propose a graph neural network-based facial palsy evaluation framework. Compared to digital images, graphs have the advantage of only encoding the facial shape in them while disregarding less relevant features like colour information. Facial landmarks are extracted and are taken as nodes to construct a facial graph. The nodes are then connected with edges through simple triangulation. These facial graphs are then fed into a graph convolutional network for facial palsy analysis. We test our proposed method on two publicly available datasets and compare its performance with three state-of-the-art methods based on convolutional neural networks. The experimental results show our proposed method either outperforms or performs on par with the state-of-the-art methods.