A new and flexible ray-tracing procedure for calculating astronomical refraction is outlined and applied to the US1976 standard atmosphere. This atmosphere is generalized to allow for a free choice of the temperature and pressure at sea level, and in this form it has been named the modified US1976 (MUSA76) atmosphere. Analytical expressions and numerical procedures are presented for calculating dry-air refractions and for the water-vapor correction. Results for all apparent altitudes are presented and compared with The Star Almanac for Land Surveyors (1951), The Nautical Almanac (1958), and the Pulkovo tables (Refraction Tables of the Pulkovo Observatory, 1985). Dependences on sea-level pressure, temperature, and temperature gradient and on humidity are discussed.