Context: The Radiation Assessment Detector (RAD) on the Mars Science Laboratory (MSL) has been measuring the radiation environment on the surface of Mars since August 6th 2012. MSL-RAD is the first instrument to provide detailed information about charged and neutral particle spectra and dose rates on the Martian surface, and one of the primary objectives of the RAD investigation is to help improve and validate current radiation transport models. Aims: Applying different numerical transport models with boundary conditions derived from the MSL-RAD environment the goal of this work was to both provide predictions for the particle spectra and the radiation exposure on the Martian surface complementing the RAD sensitive range and, at the same time, validate the results with the experimental data, where applicable. Such validated models can be used to predict dose rates for future manned missions as well as for performing shield optimization studies. Methods: Several particle transport models (GEANT4, PHITS, HZETRN/OLTARIS) were used to predict the particle flux and the corresponding radiation environment caused by galactic cosmic radiation on Mars. From the calculated particle spectra the dose rates on the surface are estimated. Results: Calculations of particle spectra and dose rates induced by galactic cosmic radiation on the Martian surface are presented. Although good agreement is found in many cases for the different transport codes, GEANT4, PHITS, and HZETRN/OLTARIS, some models still show large, sometimes order of magnitude discrepancies in certain particle spectra. We have found that RAD data is helping to make better choices of input parameters and physical models. Elements of these validated models can be applied to more detailed studies on how the radiation environment is influenced by solar modulation, Martian atmosphere and soil, and changes due to the Martian seasonal pressure cycle. By extending the range of the calculated particle spectra with respect to the experimental data additional information about the radiation environment is gained, and the contribution of different particle species to the dose is estimated.