This paper presents a semantic rule-based system for the composition of successful algorithmic pathways capable of solving medical computational problems (MCPs). A subset of medical algorithms referring to MCP solving concerns well-known medical problems and their computational algorithmic solutions. These solutions result from computations within mathematical models aiming to enhance healthcare quality via support for diagnosis and treatment automation, especially useful for educational purposes. Currently, there is a plethora of computational algorithms on the web, which pertain to MCPs and provide all computational facilities required to solve a medical problem. An inherent requirement for the successful construction of algorithmic pathways for managing real medical cases is the composition of a sequence of computational algorithms. The aim of this paper is to approach the composition of such pathways via the design of appropriate finite-state machines (FSMs), the use of ontologies, and SWRL semantic rules. The goal of semantic rules is to automatically associate different algorithms that are represented as different states of the FSM in order to result in a successful pathway. The rule-based approach is herein implemented on top of Knowledge-Based System for Intelligent Computational Search in Medicine (KnowBaSICS-M), an ontology-based system for MCP semantic management. Preliminary results have shown that the proposed system adequately produces algorithmic pathways in agreement with current international medical guidelines.