Exact determination of needle tip position is obsolete for interventional procedures under control of magnetic resonance imaging (MRI). Exact needle tip navigation is complicated by the paramagnetism of microsurgical instruments: Local magnetic field inhomogeneities are induced resulting in position encoding artifacts and in signal voids in the surrounding of instruments and especially near their tips. The artifacts generated by the susceptibility of the material are not only dependent on the material properties themselves and on the applied MRI sequences and parameters, but also on the geometric shape of the instruments and on the orientation to the static magnetic field in the MR unit. A numerical model based on superposition of induced elementary dipole fields was developed for studying the field distortions near paramagnetic needle tips. The model was validated by comparison with experimental data using field mapping MRI techniques. Comparison between experimental data and numerical simulations revealed good correspondence for the induced field inhomogeneities. Further systematic numerical studies of the field distribution were performed for variable types of concentric and asymmetric tip shapes, for different ratios between tip length and needle diameter, and for different orientations of the needle axis in the external static magnetic field. Based on the computed local inhomogeneities of the magnetic field in the surroundings of the needle tips, signal voids in usual gradient echo images were simulated for a prediction of the artifacts. The practically relevant spatial relation between those artifacts and the hidden tip of the needle was calculated for the different tip shapes and orientations in the external field. As needle tip determination is crucial in interventional procedures, e.g., in taking biopsies, the present model can help to instruct the physician prior to surgical interventions in better estimating the needle tip position for different orientations and needle tip shapes as they appear in interventional procedures. As manufacturing prototypes with subsequent measurements of artifacts in MRI are a costly procedure the presented model may also help to optimize shapes of needle tips and of other parts of MR-compatible instruments and implants with low expense prior to production if some shape parameters can be chosen freely.