The problem of beam waves propagating through a turbulent layer is studied by using both the stochastic and the deterministic approaches. In the statistical approach exact analytical expressions of beam wander and spread are derived for the turbulence with Shkarofsky spectrum by using phase screen model. The beam spread is found to be dependent, among other factors, on the spectral index of the power law spectrum. In the deterministic approach, the beam wave is propagated through a numerically simulated ionospheric bubble. Hot spots in the intensity and fast fluctuations in the phase are found to appear across the beam. Numerical examples are given. Applications to various transionospheric beam wave systems are discussed.