A new method for optimisation of the topology of engineering systems is proposed, based on reliability allocation by minimising the total cost - the sum of the cost for building the system and the risk of failure. The essence of the proposed method can be summarised in three steps: developing a system topology with the maximum possible reliability; reducing the resultant system to a system with generic components, for each of which several alternatives exist; and a third step that involves reliability allocation minimising the total cost. A heuristic optimisation algorithm and an exact recursive algorithm are also proposed. Central to the proposed methods is an efficient algorithm for determining the probability of system failure. The proposed algorithms are generic and applicable to any engineering system. They are very efficient for topologically complex reliability networks containing a large number of nodes.