This thesis deals with development and evaluation of the three dimensional, nonstationary ocean model FEOM_0 (basic version of the Finite Element Ocean Model FEOM). This model is based on the Finite Element Method (FEM) which allows for the use of unstructured grids with variable resolution. The first part of the thesis introduces the governing equations, the mathematical formulation as well as the discretisation using FEM. After introducing the discrete form of the equations some details on the numerical implementation are given.The second part of the thesis contains applications of FEOM_0 to different oceanographic tasks under idealised conditions. Comparisons to analytical results as well as to results of other numerical models in corresponding experiments are presented.The first application investigates the propagation of waves in a stratified ocean. The model shows nice correspondence to theoretically obtained wave properties as well as to results of the Modular Ocean Model (MOM). The second investigation considers the wind driven ocean circulation, especially the resulting vertical structure of the flow field. The influence of topography is examined, the results coincide with the predictions of linear theory. Finally an idealised overflow scenario is investigated. The flow of dense water on a slope poses a special problem for numerical ocean models. An international intercomparison study (DOME: Dynamics of Overflow Mixing and Entrainment) was conceived in order to gain insight into the capabilities of different numerical models in reproducing this process. FEOM_0 is applied to the idealised DOME setup with and without interior density stratification. In case of a homogeneous interior a variability in the overflow rate of several days shows up, the model gives a reasonable path of the plume and reproduces the theoretically obtained dependence of the overflow transport on Coriolis parameter and density structure.