We have pursued two different methods to analyze the old stellar population near the Galactic plane, using data from the 2MASS survey. The first method is based on the isolation of the red clump giant population in the color-magnitude diagrams and the inversion of its star counts to obtain directly the density distribution along the line of sight. The second method fits the parameters of a disc model to the star counts in 820 regions. Results from both independent methods are consistent with each other. The qualitative conclusions are that the disc is well fitted by an exponential distribution in both the galactocentric distance and height. There is not an abrupt cut-off in the stellar disc (at least within R<15 kpc). There is a strong flare (i.e. an increase of scale-height towards the outer Galaxy) which begins well inside the solar circle, and hence there is a decrease of the scale-height towards the inner Galaxy. Another notable feature is the existence of a warp in the old stellar population whose amplitude is coincident with the amplitude of the gas warp. It is shown for low latitude stars (mean height: |z| ~ 300 pc) in the outer disc (galactocentric radius R> 6 kpc) that: the scale-height in the solar circle is hz(Rsun)=3.6x 10-2 Rsun, the scale-length of the surface density is hR=0.42 Rsun and the scale-length of the space density in the plane (i.e. including the effect of the flare) is H=0.25 Rsun. The variation of the scale-height due to the flare follows roughly a law hz(R)~ hz(Rsun) exp (R-Rsun)/([12-0.6R(kpc)] kpc) (for R<~ 15 kpc; Rsun=7.9 kpc). The warp moves the mean position of the disc to a height zw=1.2x 10-3 R(kpc)5.25sin (phi +5o ) pc (for R<~ 13 kpc; Rsun=7.9 kpc).