The purpose of this study was to investigate and analyze the elementary teachers' views and students' views about the difficulties in teaching and learning on open inquiry activities of elementary school science. Semi-structured interviews were conducted individually with three elementary teachers who have serviced more than three years, and with twenty four elementary students attending schools located in Cheongju City. And their anecdotes were collected and analyzed. The interview questions were developed through Seidman's steps to acquire the reliability in the interview data. From the interviews and anecdotes, we found that elementary teachers' views about the difficulties of teaching open inquiry activities: the difficulties of teaching in finding inquiry problem and planning inquiry, the difficulties of managing group activities, the difficulties of managing class hours for inquiry, the lack of the students' inquiry abilities, and problems on students' affective characteristics. And the students have the views about the difficulties in doing open inquiry activities: the difficulties of finding inquiry problem and planning inquiry, being unaccustomed to write reports, the troubles with investigating, problems on affective characteristics, the difficulties of joining in a group, and the lack of inquiry abilities. The teachers give suggestions for effective application of the open inquiry activities: first, the teachers must encourage students' emotion and will in doing open inquiry activities, second, there must be the steady inquiry teaching and learning in ordinary elementary science classes. Based on the results, this study suggested that elementary teachers should concern specially about students' being unaccustomed to write reports and the troubles in doing scientific investigation.