The present paper introduces a case-based design with soft computing (Case-DeSC) system that uses soft computing techniques for addressing parametric design problems. Design case representation relies on digraphs of design parameters, supported by fuzzy preferences on specific parameters’ values and weighting factors, which capture the parameters’ relative importance. The final design solution is either extracted via a genetic algorithm that searches for the solution with the maximum aggregated preference, or it is retrieved by a competitive neural network. This neural network utilizes the medium of the maximum or the centroid of the assigned fuzzy preferences as similarity measures and it is trained by utilizing the available cases in the case base. Several functionalities are incorporated to the proposed system (case selection through aggregation of fuzzy preferences, case adaptation through genetic optimization with retrieved solutions used as initial population, multi-layered neural networks trained with retrieved cases used for adaptation tasks etc.). The system is evaluated through an example case of parametric design of an oscillating conveyor.