Brachytherapy is a form of radiation therapy using sealed radiation sources inserted within or in the vicinity of the tumor of, e.g., gynecological, prostate or head- and neck cancers. Accurate dose calculation is a crucial part of the treatment planning. Several reviews have called for clinical software with model-based algorithms that better take into account the effects of patient individual distribution of tissues, source-channel and shielding attenuation than the commonly employed TG-43 formalism which simply map homogeneous water dose distributions onto the patient. In this paper we give a comprehensive and thorough derivation of such an algorithm based on collapsed cone point-kernel superposition, and describe details of its implementation into a commercial treatment planning system for clinical use.A brachytherapy version of the collapsed-cone algorithm using analytical raytraces of the primary photon radiation followed by successive scattering dose calculation for once- and multiply scattered photons is described in detail, including derivation of the corresponding set of recursive equations for energy transport along cone axes/transport lines and the coupling to clinical source modeling. Specific implementation issues for setting up of the calculation grid, handling of intravoxel gradients and voxels partly containing non-patient applicator material are given.Sample runs for two clinical cases are shown, one being a gynecological application with a tungsten-shielded applicator and one a breast implant. These two cases demonstrate the impact of improved dose calculation versus TG-43 formalism.Use of model-based dose calculation algorithms for brachytherapy taking the three-dimensional treatment geometry into account increases the dosimetric accuracy in planning and follow up of treatments. The comprehensive description and derivations provided gives a rigid background for further clinical, educational and research applications.