The purpose of the study was to compare the deficit profiles of two important types of mathematics difficulties. Three cognitive measures (working memory, processing speed, and reasoning), two mathematics measures (numerical facts retrieval and mathematics vocabulary), and reading comprehension were assessed among 237 Chinese fourth-grade students, among whom 28 were classified as students with only computational difficulties (CD), 34 were classified as having only word problem-solving difficulties (WPD), 20 were classified as students with computational and word problem-solving difficulties (CD + WPD), and 43 typically developing (TD) peers. Multivariate analysis showed that, compared with TD, CD was associated with weakness in numerical working memory; WPD was associated with weakness in reading comprehension; both CD and WPD were associated with weakness in mathematics vocabulary. However, CD and WPD did not differ from each other on any of those profiling measures. Implications for understanding mathematics competence and identification of mathematics difficulties are discussed.