Kupyna was approved as the new Ukrainian hash standard in 2015. In this paper, we show several pseudo-preimage attacks and collision attacks on Kupyna. Due to the wide-pipe design, it is hard to construct pseudo-preimage attacks on Kupyna. Combining the meet-in-the-middle attack with the guess-and-determine technique, we propose some pseudo-preimage attacks on the compression function for 5-round Kupyna-256 and 7-round Kupyna-512. The complexities of these two pseudo-preimage attacks are 2229.5 (for 5-round Kupyna-256) and 2499 (for 7-round Kupyna-512) respectively. Regarding the collision attack, we can not only construct a collision attack on the 7-round Kupyna-512 compression function with a complexity of 2159.3, but also construct a collision attack on the 5-round Kupyna-512 hash function with a complexity of 2240.