The orbital evolution of several groups of relatively small asteroids (of about several hundreds meters in size) is investigated by numerical integration, with solar radiation pressure effects taken into account. Basic equations are written in the frame of the three-body problem (Sun-planet-asteroid) together with the Solar System planetary perturbations. Numerical integration was carried out to model objects with diverse physical properties and orbital parameters. Three resonance regions with Jupiter (2:1, 3:2, 1:1) and one region with the Earth (1:1) were considered. Initial conditions for integration were chosen to correspond to real relationships in asteroid belt. It was discovered that solar radiation pressure effects increase significantly with orbital eccentricity for a given asteroid orbit, no matter how strong all other perturbing actions are. Maximal variations of orbital elements occur near the above-mentioned resonance regions with planets. For example, the derived estimates show that the total variation of the distance between an asteroid's non-perturbed orbit and the orbit as perturbed by solar radiation pressure force is as high as 103 km over 100 years for Jupiter and (1-4)×103 km for the Earth (where solar radiation is more intensive). In terms of the actual asteroid hazard for the Earth, the estimated time until a hazardous close approach (of about the Earth one radius) is 10-10000 years when solar radiation pressure is taken into account.