Existence and multiplicity results for nodal solutions are obtained for the fourth-order boundary value problem (BVP) u ( 4 ) ( t ) = f ( t , u ( t ) ) , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ′ ′ ( 0 ) = u ′ ′ ( 1 ) = 0 , where f : [ 0 , 1 ] × R → R is continuous. The critical point theory and admissible invariant sets are employed to discuss this problem.