The radionuclide levels observed at present in the marine environment are very low, therefore high sensitive spectrometric systems are required for carrying out oceanographic investigations. The present-state-of-the-art carefully designed low-level HPGe gamma-spectrometers, which do not operate underground, have a dominating background component induced by cosmic rays, mostly by cosmic muons. High energy cosmic rays can initiate a large number of physical processes leading to background induction. Analytic solutions for describing these processes are not available and therefore, a Monte Carlo simulation is necessary. The development of a simulation code for background induction is useful for the optimisation of a counting system in respect to its background characteristics. It enables to assert the background before the system is built and also to perform systematic investigation of the influence of various parameters on the background of the detector. The GEANT code has been selected from the codes systems facilitating the simulation of the passage of particles through matter, as it best meets the requirements for simulations with high-energy muons. The obtained results show that the background depends most significantly on the thickness, the size and lining of the shield. Lead shielding of 15 cm thick has been found to be the optimum shielding for most applications. It is not advisable to build an unnecessarily large shield. A shield with removable lining would be the best as the lining can be removed from applications where the lead X-rays are not a disturbing influence.