Ray dynamics in a number of simple range‐dependent underwater acoustic waveguides was examined previously. It has been shown that, in such environments, at least some ray trajectories exhibit chaotic behavior, i.e., exponential sensitivity to initial conditions. This phenomenon is called ray chaos. In the present study, properties of the solution to the parabolic wave equation are examined in a bottom interacting shallow water environment in which ray trajectories are known to be predominantly chaotic. An attempt is made to determine whether the exponential sensitivity associated with ray chaos carries over to finite frequency wave fields. This phenomenon, whose existence is in question, is called wave chaos. In the search for wave chaos, 2‐, 4‐, 8‐, and 16‐kHz wave fields have been used to investigate the spreads in angle and depth of an initially narrow sound beam (these spreads grow exponentially in range under chaotic conditions according to ray theory if the initial beam is sufficiently narrow); the feasibility of back‐propagating sound fields (at ranges beyond some “predictability horizon” chaotic ray trajectories cannot be traced backwards to recover their initial conditions); and several measures of wave field complexity versus range (the complexity of a chaotic geometric wave field grows exponentially in range). In no case was exponential sensitivity, or any associated lack of predictability, observed in the finite frequency wave fields. In other words, no evidence that wave chaos exists was found.