If you think it might be blocked with cogealed fat from cooking you might try this slightly dangerous way of unblocking - it worked for me.
Buy some caustic soda - remove as much water from the sink as possible - clean the trap and reassemble then poor in some hot water and stir in some caustic soda. Take care it causes chemical burns to skin and removes paint very easily. Do not use too much soda else the solution will become saturated and the excess soda will form its own rock hard plug. Read the packet.
Give it 20 to 30 minutes or even an hour. The caustic soada mix will eat away the fat and clear the blockage. Wear rubber gloves, safety specs and old clothes.
Peccavi, November 2008