This descriptive survey study aimed to examine gifted students' success and strategic flexibility in non-routine problem solving. The study group consisted of 50 gifted students. A test consisting of seven problems was used to collect data. Answers were assessed in terms of correctness and strategy use. Flexibility was evaluated based on the use of appropriate strategies, intra-task flexibility, and inter-task flexibility. Descriptive statistics, Pearson's correlation coefficient and one-way ANOVA were used for analysis of the data. Students displayed an above-average performance in solving problems and strategy use. Students' intra-task flexibility was low, whereas their inter-task flexibility was high. There was a high correlation between flexibility and success. While success differed according to grade level, there was no significant difference between grades in terms of flexibility. Results are discussed in terms of their implications related to education, and recommendations aimed at mathematics education environments and curricula are made.