The Mechanical Waves Conceptual Survey (MWCS), presented in 2009, is the most important test to date that has been designed to evaluate university students' understanding of four main topics: propagation, superposition, reflection, and standing waves. In a literature review, we detected a significant need for a study that uses this test as an assessment tool and presents a complete analysis of students' difficulties on the test. This article addresses this need. We administered the MWCS at a private university in Mexico to 541 students. In this article, we present a complete description of these students' performance on the test, a description of their main difficulties, an elaboration of these main difficulties in terms of students' inappropriate conceptions, and recommendations for instruction based on the results obtained by the test. Our analyses may be used by instructors and researchers who intend to use the MWCS or create new instructional material.