Drains built with corrugated pipe can be difficult to clean, especially if they're clogged with an obstruction.
If the drain is on the small side, you can sometimes get good results by flushing the pipe with warm water. This works particularly well if grease is contributing to the problem.
There are several products available that claim to clean drain pipes—it is worth trying one of them if the water doesn’t work. Follow the instructions very carefully to get the best results.
If the pipe isn't very long, you may be able to use a wide bottle brush attached to a flexible rod. The bottle brush is soft and the bristles will travel through the corrugations. Sometimes it's effective to push the brush all the way through the pipe and then, while flushing the pipe with water, move the brush backwards and forwards. This way you will keep new blocks from forming as you flush the pipe.
There are specialist companies who will clean a corrugated plastic drain pipe, so if you get too frustrated, you can always outsource this yucky project.