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A distributed computing system is able to perform data computation and distribution of results at the same time. Computing systems consist of many machines, which jointly constitute a large computation power that would not be available on a single machine. The input task is divided into blocks, which are then sent to system participants, which offer their resources in order to perform calculations. The computing of a block produces a partial result, which is sent back by the participant to the task manager (usually one central node) where all partial results are combined into the final result. In the case when system participants want to get the final result, the central node may become overloaded, especially if many nodes will request the result at the same time. In this paper we propose a novel distributed computation system, which does not use the central node as the source of the final result, but assumes that partial results are sent between system participants. This way we avoid the overload of the central node, as well as the network congestion. There are two types of distributed computing systems: grids and public computation systems (called also ‘Peer-to-Peer computing systems’). In this work we focus on the latter case. Consequently, we assume that the computing system works on the top of an overlay network. We present a complete description of the P2P computing system, considering both computations and result distribution. To verify the proposed architecture we use our own simulator. The obtained results show the system performance expressed by the operation cost for various types of network flows: unicast, anycast and Peer-to-Peer. Moreover, the simulations prove that our computing system provides about 66 % lower cost comparing to a centralized computing system