Abstract In this work we study the electron‐phonon interaction in GaAs/AlGaAs double‐dot systems for cylindrical and spherical geometries with finite confinement, coupled by a tunnelling barrier and an external dc electric field. The eigenenenergies and envelope wave functions are numerically obtained for different values of the external bias. We study the effects of field and the dots‐shape on the relaxation rates of electronic transitions between double‐dot states by electron‐acoustic phonon and electron‐optical phonon interaction. We found the piezoelectric interaction to be small compared with the deformation potential one, and the spherical more convenient than the cylindrical geometry to reduce the electron‐phonon decay rates. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)