We consider the Riemann problem for isentropic van der Waals fluids, where LeFloch’s concept of nonclassical shock waves is studied. Motivated by [3, 32], we study all types of nonclassical shocks including shocks that correspond to the traveling waves of an autonomous system of differential equations with four equilibria resulted from a diffusive-dispersive model. Moreover, the range of kinetic relation is extended to the whole admissible nonclassical shock set. Corresponding to each of the two inflection points of the pressure function we can define a kinetic function. The kinetic functions may not be monotone. It is very interesting that there could be nonclassical shocks that satisfy both a kinetic relation and the Lax shock inequalities. It turns out that nonclassical Riemann solutions may form a two-parameter family of solutions. This raises an open question for the study on the selection of a unique nonclassical solution.