We investigate the accuracy of the frozen-flow approximation (FFA), re
cently proposed by Matarrese et al., for tracing of the non-linear evo
lution of cosmological density fluctuations under gravitational instab
ility. We compare a number of statistics between results of the FFA an
d N-body simulations, including those used by Melott, Pellman & Shanda
rin to test the Zel'dovich approximation. The FFA performs reasonably
well in a statistical sense (for example, in reproducing the counts-in
-cells distribution) at small scales, but it does poorly in the cross-
correlation with N-body simulations, which means that it is generally
not moving mass to the right place, especially in models with high sma
ll-scale power.