The shear wave attenuation (Q-1) in the crust beneath the northeastern US and Scandinavia is determined as a function of depth and frequency using theoretical modeling of complete waveforms in comparison with observed data. To determine attenuation in the upper crust of the northeastern US, short period (0.25<T<2 sec) Rg waves recorded by linear arrays of seismometers are used. For Scandinavia Rg and Lg waves are combined to extend the investigation into the deeper crust. The combination of Rg waves and short period (T<1.0 sec) Lg waves makes it possible to determine attenuation as a function of depth and frequency in the crust, parameterized as Q=Q0f&zgr;. To match the observations, theoretical models for three mechanisms that contribute to attenuation in the crust-frequency independent anelastic (Qa-1), and frequency dependent fluid flow (Qf-1) and scattering (Qs-1)-are considered. The best fitting models require low Q (Q0<100) in the shallow crust that increases with increasing frequency as f0.5 above 1 Hz. In the middle crust between about 2 to 10 km depth Q is moderate (100<Q0<500) with a frequency depedence of f1. In the lower crust, the attenuation is very low (Q≥500) and its frequency dependence is difficult to establish. The low intrinsic Q, and the frequency dependence, in the uppermost crust can be explained by fluid flow in fractures. In the middle crust the frequency dependence suggest scattering. The increase of Q in the lower crust is most likely due to annealing of microcracks under pressure and temperature as observed in the laboratory. ¿ American Geophysical Union 1990