In this dissertation work, a computer simulation model based on the Geant4 simulation package has been designed and developed to study the energy deposition and track structures of cosmic muons and their secondary electrons in tissue-like materials. The particle interactions in a cubic water volume were first simulated. To analyze the energy deposition and tracks in small structures, with the intention of studying the energy localization in nanometric structures such as DNA, the chamber was sliced in three dimentions. Validation studies have been performed by comparing the results with experimental, theoretical, and other simulation results to test the accuracy of the simulation model. A human body phantom in sea-level muon environment was modeled to measure the yearly dose to a human from cosmic muons. The yearly dose in this phantom is about 22 millirems. This is close to the accepted value for the yearly dose from cosmic radiation at sea level. Shielding cosmic muons with a concrete slab from 0 to 2 meters increased the dose received by the body. This dissertation presents an extensive study on the interactions of secondary electrons created by muons in water.