The West African Examination Council chief examiners’ reports repeatedly indicated that B.E.C.E. and W.A.S.S.C.E. candidates have been exhibiting weaknesses in locating points, plotting points and reading rigid motion graphs, hence the need for the conduct of this study to determine the factors responsible for students’ weakness in rigid motion. This qualitative study employed a case study design using a sample size of sixteen (16) comprising five B.E.C.E. candidates, five W.A.S.S.C.E. candidates and six experienced mathematics teachers who have taught mathematics for at least seven years. Purposive and simple random sampling techniques were employed in the selection of the sample size. Interview guide was used to collect data for the study and the collected data was analysed thematically. It was found that little or late exposure of students to the topic, lack of teaching and learning materials and rote learning or memorization were contributory factors to students’ weakness in rigid motion. It was therefore recommended that the mathematics curriculum be structured in a way that students will gain the needed exposure in rigid motion and other graph related topics as early as possible. Also, schools, Ghana Education Service, the government, philanthropists and all stakeholders in education should come to the aid of teachers and students by providing graph boards, laptops and projectors for teachers and also providing graph books for students to enable them have frequent practice in rigid motion and other graph related topics.