In the field of maxillofacial surgery, there is a huge demand from surgeons to be able to pre-operatively predict the new facial outlook after surgery. Besides the big interest for the surgeon during the planning, it is also an essential tool to improve the communication between the surgeon and his patient. In this work, we compare the usage of four different computational strategies to predict this new facial outlook. These four strategies are: a linear Finite Element Model (FEM), a non-linear Finite Element Model (NFEM), a Mass Spring Model (MSM) and a novel Mass Tensor Model (MTM). For true validation of these four models we acquired a data set of 10 patients who underwent maxillofacial surgery, including pre-operative and post-operative CT data. For all patient data we compared in a quantitative validation the predicted facial outlook, obtained with one of the four computational models, with post-operative image data. During this quantitative validation distance measurements between corresponding points of the predicted and the actual post-operative facial skin surface, are quantified and visualised in 3D. Our results show that the MTM and linear FEM predictions achieve the highest accuracy. For these models the average median distance measures only 0.60 mm and even the average 90% percentile stays below 1.5 mm. Furthermore, the MTM turned out to be the fastest model, with an average simulation time of only 10 s. Besides this quantitative validation, a qualitative validation study was carried out by eight maxillofacial surgeons, who scored the visualised predicted facial appearance by means of pre-defined statements. This study confirmed the positive results of the quantitative study, so we can conclude that fast and accurate predictions of the post-operative facial outcome are possible. Therefore, the usage of a maxillofacial soft tissue prediction system is relevant and suitable for daily clinical practice.