The class of generalized crack distribution has been effectively used in loss severity modelling due to its flexibility and the ability to fit heavy-tailed data. In this talk, a bivariate extension of the three-parameter generalized crack distribution will be discussed. Based on a mixture model specification, the constructed model renders a flexible distribution family which can fit various distribution shapes including heavy-tailed ones, yet being tractable in simulation and estimation. Some basic properties such as the conditional distribution and the measures of association will be discussed, and a method of parameter estimation will be illustrated with a model fitting exercise on a real catastrophic loss data set.