Description Logics (DLs) are a family of logic-based knowledge representation formalisms, which can be used to develop ontologies in a formally well-founded way. The standard reasoning service of subsumption has proved indispensable in ontology design and maintenance. This checks, relative to the logical definitions in the ontology, whether one concept is more general/specific than another. When no subsumption relationship is identified, however, no information about the two concepts can be given. This work extends from an existing work on similarity measure in ELH to the more expressive description logic ALEH. We introduce generalizations of the notion of normalization and homomorphism in ALEH which are then employed at the heart of our semantic similarity measure. The proposed similarity measure computes a numerical degree of similarity between two ALEH concept descriptions despite not being in the subsumption relation. 204 Suntisrivaraporn, B. and Tongphu, S. A Structural Subsumption based Similarity Measure for the Description Logic ALEH .