Abstract. Relativistic particles entering the Earth's magnetosphere, i.e. cosmic rays and solar energetic particles, are of prime space weather interest because they can affect satellite operations, communications, and the safety of astronauts and airline crews and passengers. In order to mitigate the hazards that originate from such particles one needs to predict the cutoff latitudes of such particles as a function of their energies and the state of the magnetosphere. We present results from a new particle tracing code that is used to determine the cutoff latitudes of 8-15Men^-1 alpha particles during the 23/24 April, 1998 geomagnetic storm and the preceding quiet time. The calculations are based on four different geomagnetic field models and compared with SAMPEX observations of alpha particles in the same energy range. The geomagnetic field models under consideration are: (i) the International Geomagnetic Reference Field (IGRF) model, (ii) the Tsyganenko "89" model (T89c), (iii) the Tsyganenko "96" model (T96), and (iv) a global magnetohydrodynamic (MHD) model of Earth's magnetosphere. Examining 11 SAMPEX cutoff latitude observations we find that the differences between the observed and the predicted cutoff latitudes are 2.3° ± 2.0° (mean) and 7.9° (maximum difference) for the IGRF model; 3.9° ± 2.4° (mean) and 6.9° (maximum difference) for the T89c model; 4.0° ± 1.4° (mean) and 5.5° (maximum difference) for the T96 model; and 2.5° ± 1.7° (mean) and 7.0° (maximum difference) for the MHD model. All models generally predict cutoff latitudes equatorward of the SAMPEX observations. The MHD model results also show steeper cutoff energy gradients with latitude compared to the empirical models and more structure in the cutoff energy versus latitude function, presumably due to the presence of boundary layers in the MHD model.