The transport of neutral hydrogen atoms in a hydrogen plasma slab is considered. After making a reasonable approximation for the charge exchange rate, analytic solutions for the neutral distribution function are obtained which depend on one spatial and three velocity variables. To obtain these, a condition must be imposed that implies uniform electron and ion temperatures. Specular reflection of the neutrals at the boundaries is considered. Solutions associated with the diffusion approximation are also given and the condition for its validity is discussed. The solutions are evaluated for the case of Maxwellian ion distribution functions.