Stagnation flows have been used in many studies as fair approximations of the flow field toward a flat collector, suitable for calculation of particle deposition rates. In particular, several analytical solutions for stagnation flows are widely used to model the flow over workbenches in clean rooms, and for calculating particle deposition on semiconductor wafers. It is shown that these solutions inadequately describe the flow velocity field either far from the collector surface or in its vicinity. Trajectories of diffusionless particles, calculated on the basis of these solutions, yield particle deposition efficiency as a quantity dependent on the particle initial distance (height) from the surface. In this study a physically realistic analytical model for the stagnation flow field over a finite flat obstacle is proposed. The flow field is approximated by a superposition of several basic solutions of potential and viscous stagnation flows. It provides an adequate description of the air velocity both far from and in the proximity of the surface. This flow field compares favorably with experimental data for air velocities collected in clean rooms over workbenches. The proposed flow field is incorporated in a general model of motion of nonspherical particles in vertical stagnation flows over a flat finite obstacle. This model is used to simulate trajectories of diffusionless aerosol particles, to revise theoretical results on deposition efficiencies of spherical particles obtained in previous studies, and to establish their range of validity. Trajectories of spherical particles are found to possess forms, enabling definition and calculation of height-independent deposition efficiency. Calculated deposition efficiencies are compared with experimental data on particle deposition, collected in clean rooms and during sampling. Comparable calculations for elongated particles are presented in a companion paper (Part II).