The motion of diffusionless elongated spheroidal particles in vertical stagnation flow over a flat collector of a finite size is modelled by calculating hydrodynamic forces and torques acting on a rotating and translating particle. Far above the deposition surface, particle motion is governed by its far upstream initial orientation and geometry. In close vicinity to the surface, where a viscous boundary layer prevails, particles are shown to settle down vertically due to gravity. It is found that the deposition flux of spheroidal particles which are uniformly distributed far above the surface is equal to the flux of spheres with the same settling velocity. On the other hand, randomly oriented spheroids discharged from a point source near the stagnation centerline tend to deposit in the peripheral part of the collector surface. This is in contrast with the comparable behavior of spherical particles, which deposit in a single point on the collector surface. Effects of the particle geometry, inertial and gravitational forces, initial orientation, and flow parameters on particle deposition are studied by computing particle trajectories. An approximate method is proposed for trajectory calculation, in which particle orientation is frozen and equal to the initial orientation. It is shown that trajectories of the equivalent spheres (having equal volume, or average hydrodynamic resistance, or sedimentation velocity) considerably differ from the true trajectories of spheroidal particles. Significance of the obtained results is discussed in relation to various types of stagnation flows involving aerosol deposition processes and, in particular, to clean room applications.