This study aims to investigate a construct of reading comprehension of geometry proof (RCGP). The research aims to investigate (a) the facets composing RCGP, and (b) the structure of these facets. Firstly, we conceptualize this construct with relevant literature and on the basis of the discrimination between the logical and the epistemic meanings of an argument, then assemble the content of RCGP from literature and propose a hypothetical model of RCGP. Secondly, mathematicians and mathematics teachers are interviewed for their ideas on reading mathematical proof in order to enrich the content of RCGP. Adapting the phases of reading comprehension in language, the content of RCGP is classified into six facets. Lastly, these facets are structured using the hypothetical model and then justified by students' performance in the facets of RCGP using the multidimensional scaling method. The results sustain that the structure of facets can be characterized by this conceptualized model.