||In the Software Defined Coalition (SDC), computation, communications and memory resources are distributed across multiple domains and can be used to execute analytics. It is challenging to characterize the capacity of such distributed resources because of the randomness of required resources by tasks. In this work, we derive analytical formulas for the upper bound of capacity of distributed systems with multiple resources. Resource allocation methods including random assignment, power of d choices assignment and the least occupancy first assignment are considered to help analyze and approximate the capacity of distributed SDC resources. The capacity results are useful for describing the remaining capacity of distributed resources in SDC or distributed computing systems in general. They can also be used to assist scheduling and admission decisions of distributed analytics to various resources in the systems. Numerical study is included to validate of the capacity upper bounds.