We present synthetic spectra for atmospheres in order to interpret the observed spectra of the supernova 1987A during the first few months after the initial event. Spherical symmetry and density profiles are assumed which are given by the homologous expansion of the stellar structure of a B3 supergiant. For hydrogen, up to eight levels and, for helium, 16 levels are allowed to deviate from LTE. The radiation transport is calculated consistently with the rate equations both for the continua and for the lines. Radiative equilibrium is assumed. The observed spectra and colours in the optical wavelength range can be well reproduced by pure hydrogen models during the first few weeks. The behaviour of the UV flux is due to changes in the effective temperature and the photospheric radius. For later stages, the influence of elements other than hydrogen and helium must be taken into account in order to compare the calculated and observed spectra in the optical wavelength range. Reasonable agreement between calculations and observations can be obtained with the assumption of half solar abundances for all elements but for the s-process elements Sc, Ti and Ba which are overabundant. To explain the small changes in the spectra after about 3 weeks up to 4 months, we need a total hydrogen mass of about 8 to 10 M⊙.