This work proposes a method for estimating the development cost of a software system with modular structure taking into account the target level of reliability for that system. The required reliability of each individual module is set in order to meet the overall required reliability of the system. Consequently the individual cost estimates for each module and the overall cost of the software system are linked to the overall required reliability. Cost estimation is carried out during the early design phase, that is, well in advance of any detailed development. Where a satisfactory compromise between cost and reliability is feasible, this will enable a project manager to plan the allocation of resources to the implementation and testing phases so that the estimated total system cost does not exceed the project budget and the estimated system reliability matches the required target. The line of argument developed here is that the operational reliability of a software module can be linked to the effort spent during the testing phase. That is, a higher level of desired reliability will require more testing effort and will therefore cost more. A method is developed which enable us to estimate the cost of development based on an estimate of the number of faults to be found and fixed, in order to achieve the required reliability, using data obtained from the requirements specification and historical data. Using Markov analysis a method is proposed for allocating an appropriate reliability requirement to each module of a modular software system. A formula to calculate an estimate of the overall system reliability is established. Using this formula, a procedure to allocate the reliability requirement for each module is derived using a minimization process, which takes into account the stipulated overall required level of reliability. This procedure allow us to construct some scenarios for cost and the overall required reliability. The foremost application of the outcome of this work is to establish a basis for a trade-off model between cost and reliability during the design phase of the development of a modular software system. The proposed model is easy to understand and suitable for use by a project manager.