Ionizing radiation produces both singly and multiply damaged DNA sites. Multiply damaged sites (MDS) have been implicated in radiation-induced cell killing and mutagenesis. The spatial distribution of elementary damages (strand breaks and base damages) that constitute MDS is of special interest, since the complexity of MDS has an impact on damage repair. A fast and easy-to-implement algorithm to simulate the local clustering of elementary damages produced by ionizing radiation is proposed. This algorithm captures the major trends in the DNA damage spectrum predicted using detailed track- structure simulations. An attractive feature of the proposed algorithm is that only four adjustable parameters need to be identified to simulate the formation of DNA damage. A convenient recipe to determine the parameters used in the fast Monte Carlo damage simulation algorithm is provided for selected low- and high-LET radiations. The good agreement among the damage yields predicted by the fast and detailed damage formation algorithms suggests that the small-scale spatial distribution of damage sites is determined primarily by independent and purely stochastic events and processes.