The described embodiments relate to a downhole tool that can capture a ball in a trap to prevent both upwell and downwell movement of the ball. Further, certain embodiments described herein may prevent fluid from flowing past a captured ball in either the upwell or downwell directions. Ball and seat valves incorporating such ball trap assemblies can be used to create a bi-directional plug which prevents fluid flow in either direction when the ball trap is engaged with an appropriately configured ball.