Large-scale persistent vortices are known to form easily in 2D disks via the Rossby wave or the baroclinic instability. In 3D, however, their formation and stability is a complex issue and still a matter of debate. We study the formation of vortices by the Rossby wave instability in a stratified inviscid disk and describe their three dimensional structure, stability and long term evolution. Numerical simulations are performed using a fully compressible hydrodynamical code based on a second order finite volume method. We assume a perfect gas law and a non-homentropic adiabatic flow.The Rossby wave instability is found to proceed in 3D in a similar way as in 2D. Vortices produced by the instability look like columns of vorticity in the whole disk thickness; the small vertical motions are related to a weak inclination of the vortex axis appearing during the development of the RWI. Vortices with aspect ratios larger than 6 are unaffected by the elliptical instability. They relax to a quasi-steady columnar structure which survives hundred of rotations while slowly migrating inward toward the star at a rate that reduces with the vortex aspect ratio. Vortices with a smaller aspect ratio are by contrast affected by the elliptic instability. Short aspect ratio vortices are completely destroyed in a few orbital periods. Vortices with an intermediate aspect ratio are partially destroyed by the elliptical instability in a region away from the mid-plane where the disk stratification is sufficiently large. Elongated Rossby vortices can survive a large number of orbital periods in protoplanetary disks in the form of vorticity columns. They could play a significant role in the evolution of the gas and the gathering of the solid particles to form planetesimals or planetary cores, a possibility that receives a renewed interest with the recent discovery of a particle trap in the disk of Oph IRS48.