More than a simple carrier of the genetic information, messenger RNA (mRNA) coding regions can also harbor functional elements that evolved to control different post-transcriptional processes, such as mRNA splicing, localization and translation. Functional elements in RNA molecules are often encoded by secondary structure elements. In this aticle, we introduce Structural Profile Assignment of RNA Coding Sequences (SPARCS), an efficient method to analyze the (secondary) structure profile of protein-coding regions in mRNAs. First, we develop a novel algorithm that enables us to sample uniformly the sequence landscape preserving the dinucleotide frequency and the encoded amino acid sequence of the input mRNA. Then, we use this algorithm to generate a set of artificial sequences that is used to estimate the Z-score of classical structural metrics such as the sum of base pairing probabilities and the base pairing entropy. Finally, we use these metrics to predict structured and unstructured regions in the input mRNA sequence. We applied our methods to study the structural profile of the ASH1 genes and recovered key structural elements. A web server implementing this discovery pipeline is available at http://csb.cs.mcgill.ca/sparcs together with the source code of the sampling algorithm.