In this paper, an ontology-based system (KnowBaSICS-M) is presented for the semantic management of Medical Computational Problems (MCPs), i.e., medical problems and computerised algorithmic solutions. The system provides an open environment, which: (1) allows clinicians and researchers to retrieve potential algorithmic solutions pertinent to a medical problem and (2) enables incorporation of new MCPs into its underlying Knowledge Base (KB). KnowBaSICS-M is a modular system for MCP acquisition and discovery that relies on an innovative ontology-based model incorporating concepts from the Unified Medical Language System (UMLS). Information retrieval (IR) is based on an ontology-based Vector Space Model (VSM) that estimates the similarity among user-defined MCP search criteria and registered MCP solutions in the KB. The results of a preliminary evaluation and specific examples of use are presented to illustrate the benefits of the system. KnowBaSICS-M constitutes an approach towards the construction of an integrated and manageable MCP repository for the biomedical research community.