A method of ray tracing (RT) with amplitude variations for simulating VLF wave propagation in a weakly inhomogeneous upper ionosphere and magnetosphere is discussed in detail. This ray tracing plus amplitude (RTA) technique is different from the existing ones in the selection of the most complete model with all its plasma parameters dependent on geomagnetic activity, allowance of thermal correction to the refractive index, and calculations of amplitude factors (coefficients of focusing-defocusing, polarization, and linear amplification-attenuation). The presented examples of calculations show that the introduction of the above new elements in the RT technique makes it possible to clarify the wave propagation properties and to account for numerous experimental phenomena. ¿ American Geophysical Union 1995