The nonlinear, steady state magnetohydrodynamics natural convection boundary layer flow, heat and mass transfer of an viscoelastic incompressible Jeffrey’s fluid from a vertical permeable cone with thermal radiation and heat generation/absorption effects is investigated in this article. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit finite-difference Keller box technique. The Rosseland diffusion algebraic approximation is utilized to simulate thermal radiation effects. The surface of the cones is maintained at a constant temperature and concentration with mass flux present. Excellent correlation of the present results with previous studies is obtained to validate the numerical code. The influence of Deborah number (De), ratio of relaxation to retardation times (λ), radiation parameter (F), heat generation/absorption parameter (Δ), suction/injection parameter (f w ), magnetic parameter (M) and dimensionless tangential coordinate (ξ) on velocity, temperature and concentration evolution in the boundary layer regime are examined in detail. Also, the effects of these parameters on local skin friction, heat transfer rate and mass transfer rate are investigated. © 2016, Springer India Pvt. Ltd.