In physics lectures on electromagnetic theory and mathematical methods, physics teacher candidates have some difficulties with curvilinear coordinate systems. According to our experience, based on both in-class interactions and teacher candidates' answers in test papers, they do not seem to have understood the variables in curvilinear coordinate systems very well. For this reason, the problems that physics teacher candidates have with variables in curvilinear coordinate systems have been selected as a study subject. The aim of this study is to find the physics teacher candidates' problems with determining the variables of drawn shapes, and problems with drawing shapes based on given variables in curvilinear coordinate systems. Two different assessment tests were used in the study to achieve this aim. The curvilinear coordinates drawing test (CCDrT) was used to discover their problems related to drawing shapes, and the curvilinear coordinates detection test (CCDeT) was used to find out about problems related to determining variables. According to the findings obtained from both tests, most physics teacher candidates have problems with the phi variable, while they have limited problems with the r variable. Questions that are mostly answered wrongly have some common properties, such as value. According to inferential statistics, there is no significant difference between the means of the CCDeT and CCDrT scores. The mean of the CCDeT scores is only 4.63 and the mean of the CCDrT is only 4.66. Briefly, we can say that most physics teacher candidates have problems with drawing a shape using the variables of curvilinear coordinate systems or in determining the variables of drawn shapes.