This thesis contains results of numerical investigations of magnetisation dynamics in nanostructed ferromagnetic materials. Magnetic systems have been simulated using the open source micromagnetic solver: Object Oriented Micromagnetic Framework (OOMMF), and thoroughly analysed using my own software: semargl. A systematic study of collective magnonic modes confined in 2D and 3D systems of rectangular ferromagnetic nano-elements is presented. The collective character of the excitations results from the dynamic magnetic dipole field. The magnetization dynamics of isolated rectangular elements is found to be spatially non-uniform which means that the dynamic dipolar coupling is highly anisotropic. A semi-analytical theory of collective magnonic modes has been developed to evaluate the properties of the dynamic magnetic dipole field. It was found that the theory is only valid for certain eigenmodes of the isolated element. In particular the modes where the magnetic dipole coupling between the elements is much lower than the internal energy of the corresponding eigenmodes of the isolated element. It is then demonstrated that the confinement of spin waves is strongly affected by the ground state of the system. In particular it has been found that symmetry properties of the topology of 2D arrays affect the dynamics of the strongly localised modes. The effect is found to be significant for arrays of any number of elements. At the same time the relative contribution of the localized modes to the uniform response decreases with the number of elements in the array. The dispersion relation of spin waves in 2D arrays of rectangular nano-elements has been calculated for the first time using micromagnetic simulations. The form of the dispersion is used to estimate the spatial anisotropy of the dynamic dipolar coupling. Simulations of the 3D confinement of spin waves in stacks of magnetic nano-elements have been performed. The calculation of both the dispersion and spatial profiles of the corresponding magnonic modes facilitates the investigation of the localisation of collective spin waves. Furthermore the dispersion of collective magnonic modes has been calculated for stacks of rectangular nano-elements for a range of in-plane aspect ratios. Finally, a numerical method has been developed to extract the scattering parameters of magnonic logic devices. This method has been demonstrated by applying it to the simplest possible magnonic device so that the results could be compared to an analytical expression of the scattering parameters.