We introduce copulas and their usage in shock models. The name copula derives from the latin word for 'link' or 'tie', which roughly describes their purpose. We define copulas and introduce them to the world of probability and distribution functions via the Sklar theorem. To get a clearer picture of what copulas are, we get to know some of the more famous copulas and see their visual representations in the form of spatial graphs, contour plots and scatterplots. We introduce copulas to shock models and show their usability via examples. Via shock models we introduce arrivals of shocks into systems. Based on the type and distribution of shock arrival times and number and types of components we distinguish different models. In this thesis we will get acquintanced with two-component systems, and based on effects and the distribution of shock arrival times we will define three different models. We define copulas for different shock models and through their application bind multiple univariate distribution functions into one distribution function of the system.