A theoretical investigation is made of the density field for rarefied flow through an orifice. Within the assumptions of Maxwellian velocity distribution of the gas and of diffuse reflection from the reservoir walls, exact expressions are found for the density at the center line of the effusing stream for a circular orifice and for all regions of the field for square and rectangular orifices. The density field is found to be most affected by orifice geometry in the near region. For narrow slits the effect is felt further from the orifice than for nearly square or circular geometries.