Constrained sequence alignment has been studied extensively in the past. Different forms of constraints have been investigated, where a constraint can be a subsequence, a regular expression, or a probability matrix of symbols and positions. However, constrained structural alignment has been investigated to a much lesser extent. In this paper, we present an efficient method for constrained structural alignment and apply the method to detecting conserved secondary structures, or structural motifs, in a set of RNA molecules. The proposed method combines both sequence and structural information of RNAs to find an optimal local alignment between two RNA secondary structures, one of which is a query and the other is a subject structure in the given set. The method allows a biologist to annotate conserved regions, or constraints, in the query RNA structure and incorporates these regions into the alignment process to obtain biologically more meaningful alignment scores. A statistical measure is developed to assess the significance of the scores. Experimental results based on detecting internal ribosome entry sites in the RNA molecules of hepatitis C virus and Trypanosoma brucei demonstrate the effectiveness of the proposed method and its superiority over existing techniques.