Model calculations for the photospheres of SN 1987A are presented. Spherical symmetry and density profiles are assumed to be given by the homologous expansion of the stellar structure of a B3I supergiant. For later stages the density slopes are determined. For a number of elements (H, He, C, N, O, Ne, Na, Mg, K, Ca, Ba) detailed atomic models are used. The statistical equations and the radiation transport are treated consistently as well for the lines as for the continua. In addition, line blanketing due to other elements are included under the assumption of pure scattering. The importance of a sophisticated NLTE-treatment is demonstrated. Chemical metal abundances are derived by comparing the observed and synthetic spectra. Good agreement is found if a third of solar abundance for all elements with the exception of the s-process elements is assumed. An overabundance of He by a factor of 1-2 is indicated by the models corresponding to the time before June 87. No gradient in the chemical abundances of the hydrogen rich layers has to be assumed. Up to October 87 the He abundance at the photosphere is increased to 5 times solar, i.e. the continua are formed in helium rich layers. The chemical profile indicates strong mixing processes of the different layers of the progenitor during the explosion. Additionally, pecularities of hydrogen line profiles are discussed. Mainly, they can be understood by selective line blanketing effects. The total mass of the hydrogen rich shell is estimated to amount to be 9-11 M⊙.