This thesis uses renewal theory to investigate the Lanchester-type combat attrition process. The attrition process is analysed in detail and modelled as a so-called renewal process in which times between casualties are considered to be independently and identically distributed random variables. Other random variables that can be considered in the renewal process are examined, and the distributions of these random variables are determined in order to study the behavior of attrition process. Examples with specific distribution functions are given for better understanding. Computer simulation is generated and compared with the attrition model developed. The total casualty occurence by total force is also discussed, through pooling of the single renewal processes. The total casualty occurence is shown to be a Poisson process and times between casualties to be approximately exponentially distributed for large numbers of combatants.