Abstract: The Alpha Magnetic Spectrometer, AMS, is successfully collecting data on the International Space Station since its installation on May 19, 2011. One of the main objectives of AMS is the precision measurement of high energy cosmic ray electrons and positrons. The key detector for this measurement is the Electromagnetic Calorimeter. Reconstruction of electrons and positrons in the calorimeter uses a 3-dimensional shower parametrization, which accounts for the detector specifics: finite size of the calorimeter, non-uniform efficiency of the signal collection, and saturation effects due to the electronics and due to high energy density in the active calorimeter elements. This technique provides AMS with a precision energy measurement of electrons and positrons up to several TeV as well as an excellent rejection of the proton background.