Electron trapping and acceleration have been successfully accomplished in the modified elongated betatron at University of California, Irvine. About 150 nC of electrons have been trapped and accelerated for approximately 900 musec until the betatron field reached its maximum, establishing an electron layer with approximately 80 A of circulating current and approximately 1.6 MeV energy in the cylindrical chamber. No minimum current is required to start beam trapping in the betatron. There are essentially no electron losses during the acceleration at low injection currents; the electron losses at high injection currents are probably caused by the space charge effects, resistive chamber walls, and betatron field ripple. By filling the chamber with plasma, an electron beam of approximately 120 A current and approximately 1.6 MeV energy has been observed. No instabilities have been found during the acceleration except the precessional instability, which has been effectively controlled by a toroidal magnetic field. An electron orbit simulation has been carried out and it has shown that practically no resonance instabilities can be developed in the stretched betatron because of its unique geometry and field configuration, which has been confirmed by the experiment.