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We have pursued two different methods to analyze the old stellar populationnear the Galactic plane, using data from the 2MASS survey. The first method isbased on the isolation of the red clump giant population in the color-magnitudediagrams and the inversion of its star counts to obtain directly the densitydistribution along the line of sight. The second method fits the parameters ofa disc model to the star counts in 820 regions. Results from both independentmethods are consistent with each other. The qualitative conclusions are thatthe disc is well fitted by an exponential distribution in both thegalactocentric distance and height. There is not an abrupt cut-off in thestellar disc (at least within R<15 kpc). There is a strong flare (i.e. anincrease of scale-height towards the outer Galaxy) which begins well inside thesolar circle, and hence there is a decrease of the scale-height towards theinner Galaxy. Another notable feature is the existence of a warp in the oldstellar population whose amplitude is coincident with the amplitude of the gaswarp.  It is shown for low latitude stars (mean height: |z|~300 pc) in the outerdisc (galactocentric radius R>6 kpc) that: the scale-height in the solar circleis h_z(R_sun)=3.6e-2 R_sun, the scale-length of the surface density is h_R=0.42R_sun and the scale-length of the space density in the plane (i.e. includingthe effect of the flare) is H=0.25 R_sun. The variation of the scale-height dueto the flare follows roughly a law h_z(R) =~ h_z(R_sun) exp[(R-R_\odot)/([12-0.6R(kpc)] kpc)] (for R<~15 kpc; R_sun=7.9 kpc). The warpmoves the mean position of the disc to a height z_w=1.2e-3 R(kpc)^5.25sin(phi+(5 deg.)) pc (for R<~13 kpc; R_sun=7.9 kpc).Comment: LaTEX, 20 pages, 23 figures, accepted to be published in A&

Old stellar Galactic disc in near-plane regions according to 2MASS: Scales, cut-off, flare and warp