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.1 Introduction Double quantum dots have been proposed as good candidates to the implementation of nano-devices both for optoelectronics and quantum computation [1,2]. Tunability of states and long coherence times are the main advantages of such systems [3,4]. Such properties have arose great expectation and interest about studying and controlling the decoherence processes in this kind of structure. There is an agreement that electron-phonon interactions are the main decoherence channels, since embedded in or grown on host materials, the interaction between the confined carriers and the lattice nucleus is inevitable. Former works on electron-phonon interaction have been done for GaAs double quantum dots with harmonic infinite confinement potential [4,5], and for finite confinement in rectangular dots [6]. In this work we study spherical and cylindrical dots with a finite step potential confinement. In the first place, eigenenergies and envelope wave functions are found. Having into account such transition energies, electron-optical phonon interactions are discussed. After that, decay rates of electronic transitions by electron-acoustic phonon are calculated. Finally we analyse and conclude the effects of the bias field and the dot-shape on those rates.