It happened near a pond to the rear of Blenheim Way in Castleford at about 7pm on Saturday, May 11.
The men approached the pond and used bread to bait the ducks towards them.
They then used a catapult to kill the two ducks.
Police have described both suspects as white and aged in their early twenties.
One man was described as having bright ginger hair and facial hair.
The second man was dark haired and clean shaven.
In a statement released on Facebook, the West Yorkshire Police - Wildlife & Rural Crime team said: "At about 7pm on the 11/5/2019 two males approached a pond to the rear of Blenheim Way, Castleford used bread to bait ducks closer to them. They then used a catapult to kill two ducks."Suspects both white males early twenties ...One had bright ginger hair and facial hair. Second male dark haired clean shaven. Crime number 13190244808. Any info please call 101 or email the team."
They have appealed for anyone with information to contact them.