Capabilities for turbulence calculations of the Lagrangian averaged Navier–Stokes (LANS-α) equations are investigated in decaying and statistically stationary three-dimensional homogeneous and isotropic turbulence. Results of the LANS-α computations are analyzed by comparison with direct numerical simulation (DNS) data and large eddy simulations. Two different decaying turbulence cases at moderate and high Reynolds numbers are studied. In statistically stationary turbulence two different forcing techniques are implemented to model the energetics of the energy-containing scales. The resolved flows are examined by comparison of the energy spectra of the LANS-α with the DNS computations. The energy transfer and the capability of the LANS-α equations in representing the backscatter of energy is analyzed by comparison with the DNS data. Furthermore, the correlation between the vorticity and the eigenvectors of the rate of the resolved strain tensor is studied. We find that the LANS-α equations capture the gross features of the flow, while the wave activity below the scale α is filtered by a nonlinear redistribution of energy.