The modern Einsteinian conception of space, time, matter and radiation represents a radical paradigm shift compared with the traditional Newtonian physics that underpins most primary and secondary school science. It is increasingly recognised that school education should encompass this modern paradigm to allow a seamless progression of learning throughout school education. The goal of the research presented in this paper was to test whether five core concepts of the Einsteinian paradigm could become conceptually intelligible to middle school students or whether there were intrinsic difficulties. The research was underpinned by the theoretical notion that intelligibility is a key step to the ontological conceptual changes needed for the radical shift to the Einsteinian paradigm and that conceptual change is impacted by students’ attitudes. The research was conducted in the context of a 20-lesson teaching programme based on models and analogies specifically designed for middle school students and to enable ontological conceptual change. We present an analysis of 120 14- to 15-year-old students’ conceptualisations of Einsteinian physics and their attitudes towards science as a result of this programme. Through testing before and after the programme, we found that the students possessed variable levels of prior knowledge of the core Einsteinian concepts, but near universal intelligibility of the core concepts after the programme. The strong saturation indicates that there is no intrinsic difficulty regarding intelligibility of core Einsteinian concepts at the middle school level of the participants. While the male students initially showed greater interest in physics compared with their female counterparts, the female students showed a significantly increased interest in physics after the programme. Repeatability in knowledge tests between classes given one year apart and long-term retention indicate that the programme had a lasting impact on students’ conceptual understanding.