An Abdominal Aortic Aneurysm (AAA) is a form of vascular disease causing focal enlargement of the abdominal aorta. It affects a large part of the population, and in case of rupture, has up to 90% mortality rate. Recent clinical recom- mendations suggest that people with small aneurysms should be examined 3-36 months depending on the size, to monitor morphological changes. While advances in biomechanics provide state-of-the-art spatial estimates of stress distributions of AAAs, there are still limitations in modeling its time evolution and uncertainty qualification. To date, there are a few biomechanical frameworks that utilize longitudinal medical images, which would aid physicians in detecting small aneurysms with high risk of rupture. In this study, we use longitudinal computer tomography (CT) scans of AAAs that are captured at different times to predict the spatio-temporal evolution of AAAs' shape in future time. We consider a surface of 3D AAA as a manifold embedded in a scalar field over the three dimensional space. The changes of the scalar field propagate into the changes in the surface. For this formulation, we develop our Dynamical Gaussian Process Implicit Surface (DGPIS) model based on observed surfaces of 3D AAAs as visible variables while the scalar fields are hidden fields. First of all, we utilize the concept of the implicit surface field as a parameterization-free framework to describe a 3D shape. We then use Gaussian process regression to construct the field as an observation model from CT training image data. Furthermore, we propose a dynamic model to represent the evolution of the field. Finally, we derive the predicted surface from the predicted field. Our model is deployed on a real medical data set, which indicates its effectiveness. In addition, we discuss our prediction results with respect to ones from conventional analysis techniques.