We will discuss the observed, heavily damped transversal oscillations of coronal loops. These oscillations are often modeled as transversal kink oscillations in a cylinder. Several features are added to the classical cylindrical model. In our models we include loop curvature, longitudinal density stratification, and highly inhomogeneous radial density profiles. In this paper, we will first give an overview of recently obtained results, both analytically and numerically. After that, we shed a light on the computational aspects of the modeling process. In particular, we will focus on the parallellization of the numerical codes.