The ray-tracing procedure for modeling the power deposition into electron cyclotron resonance (ECR) discharge in an axisymmetric mirror trap with longitudinal launch of microwave power is presented. To deal with cyclotron absorption for normal waves of magnetized plasma propagating nearly along the magnetic field in the vicinity of electron cyclotron frequency approximate dispersion relation has been derived using Stix components for microwave electric field. Calculations have been performed for parameters corresponding to ECR multicharge ion (MCI) source (IAP RAS) as example. It is shown that the efficient power deposition into ECR discharge within single pass of radiation through the plasma column may be provided under conditions that parasitic cyclotron resonance (before the plug) is outside the plasma volume and the electron density in the vicinity of the main resonance is undercritical. This is in a qualitative agreement with experimental results.