The aim of this study is to investigate pre-service teachers' understanding of and difficulties with some core concepts in the special theory of relativity. The pre-service teachers (n = 185) from the Departments of Physics Education and Elementary Science Education at Dokuz Eylul University (in Turkey) participated. Both quantitative and qualitative research methods were used in this study. Students' understanding of and difficulties with core elements (time, length, mass and density) were tested using a paper-and-pencil questionnaire (including four questions) and in-depth interviews after the instruction of related modern physics topics. The analyses of the collected data were based on quantitative and qualitative techniques. The results indicate that pre-service teachers at different academic levels have specific and considerable difficulties with proper time, time dilation, proper length, mass and relativistic density concepts. In this paper, the conclusions of the study and implications for physics teaching are discussed. (Contains 4 figures.)