In this paper we investigate the presence of math anxiety (MA) among University Engineering students at all levels of undergraduate study. In an effort to assess the presence and severity of MA over the course of an undergraduate degree, as well as to quantify the number of highly math anxious students in this STEM discipline, a 29-question survey was conducted in each of five levels of undergraduate Engineering students. Using non-parametric statistical methods such as Kruskal-Wallis and Mann-Whitney tests as well as pairwise proportion comparisons, MA was compared across years of study. Utilizing existing anxiety classifications of Math Evaluation Anxiety (MEA), Learning Mathematics Anxiety (LMA) and Numerical Anxiety (NA), it was found that MEA showed the highest anxiety scores, while LMA and NA remained at or below a neutral anxiety score in all years of study. MEA questions related to anticipation of evaluation and the receipt of grades revealed the highest scores and the greatest discrepancy in anxiety by year (with Year 1 students more highly anxiously than later years in nearly all cases). Although earlier research suggests that MA tapers off by grade 10, this research suggests that while first-year university students exhibit low levels of LMA and NA, they continue to exhibit high levels of MEA. This result may be in part due to the level of questions on traditional MA assessment questionnaires addressing lower level mathematical concepts (such as addition, subtraction, multiplication and division). Since students gain comfort and mastery of concepts as they use them more frequently, this study suggests that such metrics for MA must be adjusted in order to accurately assess students as they progress through later years of study.