  The use of semiclassical models based on the Strong Field Approximation (SFA)
is ubiquitous in strong field multi-photon ionization and underlies many key
developments in attosecond science, including the description of High Harmonic
Generation (HHG). However, such models are notably lacking in streaking
experiments, which use an attosecond pulse to initiate single-photon ionization
and a lower frequency infrared pulse to provide timing information. Here, we
introduce a classical Wigner propagation (CWP) method, which analogously to
semiclassical models in strong field ionization, treats the ionization step
quantum mechanically, followed subsequently by classical propagation (with
initial conditions obtained from the Wigner function) in the infrared probe
field. As we demonstrate, this method compares well with experimental data and
full two-electron quantum simulations available for helium, includes
multi-electron effects, and can be applied to molecules, where the full
solution of the time-dependent Schrodinger equation is not feasible. Applying
the CWP method to a many-atom molecule, like 2,3,3-trimethyl-butyl-2-iodide, we
find a relatively significant directional dependence of streaking delays,
indicating the importance of orientation-resolved measurements in molecules.
