The equations and boundary conditions governing tidal oscillations in a viscous, rotating, spherical atmosphere from the surface to 400 km are formulated, including model parameterizations of background winds, temperature, composition, hydromagnetic coupling, Newtonian cooling, eddy and molecular diffusion, and tidal forcing mechanisms. Excitation of tidal oscillations occurs via absorption of EUV and UV radiation in the thermosphere, H2O insolation absorption in the troposphere and lower stratosphere, O3 insolation absorption in the mesosphere, ion-neutral momentum coupling in the F region, and lunar gravitational forcing. The method of solution for the equations is outlined, and numerical convergence of the viscid model for certain test cases is verified by comparison with analytic calculations below 100 km from classical (inviscid) tidal theory. Calculated results for the solar diurnal tide from the surface to 400 km are presented and compared with rocket and radar observations. Considering the day-to-day variations that are clearly evident in the data, observations of tides by various rocket and radar techniques are in good agreement with the 'mean tidal structures' represented by the model. The greatest inconsistencies occur in the 80- to 100-km height region where the diurnal propagating tide and the in situ trapped tide are of comparable importance at mid-latitudes. The (1,1) propagating tide above 70 km is sensitively coupled to the intensity of turbulence in the tropical mesosphere as parameterized by the eddy coefficients for diffusion of momentum and heat, undoubtedly contributing to its vagarious nature. Other factors causing inconsistencies with individual observations include possible 'mode distortions' induced by background mean winds and the attempted interpretation of global data sets taken during non-overlapping time periods. Forthcoming analyses of CTOP observational periods should alleviate this latter problem and contribute to a clearer understanding of mesospheric and lower thermospheric tides.