This paper presents an implementation of the set-covering model for diagnosing psychiatric disorders. Such a model is useful as the basis for the inference mechanism of an expert system in that it provides a satisfactory solution to the difficult problem of multiple simultaneous disorders. The set covers have been formed through the 'diagonal search method' in which the combination of an element with the rest of the elements along the diagonals in the combination matrix was found to be adequate. 'Abductive logic' has been used to reach the possible final solution. Another feature of this expert system is its elicitation system. Provision has been made in the expert system for observations to be made and questions to be asked of the patient in difficult-to-elicit psychiatric signs. It makes this expert system usable by the non-expert clinicians. This has been specially designed in the context of third-world conditions. The system has been tested on cases given in the DSM-III case book with 100% success. However, the system's knowledge should be expanded and refined if it is to be used in psychiatric clinical practice.