The calibration of gamma-ray cylindrical detectors is often required in the analysis of high or low environmental samples and the homogenously distributive nuclear waste drums. Therefore, a new analytical simulation method is proposed in the present work to calculate the full-energy peak efficiencies of high-purity germanium cylindrical detectors using extended sources of low and high volumes. The sources were mounted at three different positions with respect to the detector's axis (coaxial, parallel, and perpendicular), labeled as Position 1, Position 2, and Position 3, respectively. The self-attenuation and the coincidence summing effects at low source-detector distance are also included in the algorithm. A remarkable agreement between the measured and the calculated efficiencies is achieved with discrepancies <4% for the first two positions and between 5 and 7% for the last one.