In order to determine the most effective arrangement for a network of environmental radiation monitors, their optimal location and design have been studied taking into consideration several essential characteristics of the monitors, that is, the relative frequency of wind flow towards the monitors, population density around the monitors, failure rates of monitoring equipments (the necessity for redundancy), and economical factors.The optimizations are made by introducing an objective function, which is formulated as the probability of detecting a radioactive cloud by a monitoring network in good working condition at the required time. The problem of optimum location of monitors is reduced to that of maximizing the objective function under the constraint of given budgetary limits. Optimal apportionment of redundancy for weak subsystems in the monitoring network is studied by a dynamic .programming technique of matrix type developed for the purpose.The concepts and methods developed in this paper are also applicable to the design of similar systems in other fields.