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Context. The Lyman alpha emission line of galaxies is an important tool forfinding galaxies at high redshift, and thus probe the structure of the earlyuniverse. However, the resonance nature of the line and its sensitivity to dustand neutral gas is still not fully understood.  Aims. We present measurements of the velocity, covering fraction and opticaldepth of neutral gas in front of two well known local blue compact galaxiesthat show Lyman alpha in emission: ESO 338-IG 04 and Haro 11. We thus testobservationally the hypothesis that Lyman alpha can escape through neutral gasby being Doppler shifted out of resonance.  Methods. We present integral field spectroscopy from the GIRAFFE/Argusspectrograph at VLT/FLAMES in Paranal, Chile. The excellent wavelengthresolution allows us to accurately measure the velocity of the ionized andneutral gas through the H-alpha emission and Na D absorption, which traces theionized medium and cold interstellar gas, respectively. We also presentindependent measurements with the VLT/X-shooter spectrograph which confirm ourresults.  Results. For ESO 338-IG04, we measure no significant shift of neutral gas.The best fit velocity is -15 (16) km/s. For Haro 11, we see an outflow fromknot B at 44 (13) km/s and infalling gas towards knot C with 32 (12) km/s.Based on the relative strength of the Na D absorption lines, we estimate lowcovering fractions of neutral gas (down to 10%) in all three cases.  Conclusions. The Na D absorption likely occurs in dense clumps with highercolumn densities than where the bulk of the Ly-alpha scattering takes place.Still, we find no strong correlation between outflowing neutral gas and a highLyman alpha escape fraction. The Lyman alpha photons from these two galaxiesare therefore likely escaping due to a low column density and/or coveringfraction.

Neutral gas in Lyman-alpha emitting galaxies Haro 11 and ESO 338-IG04 measured through sodium absorption