We study spin-up of a viscous electrically conducting Boussinesq fluid in a circular cylinder subject to thermal stratification and uniform axial magnetic field. The cylinder is a perfect conductor of electricity and of heat. Physical parameters are chosen to be consistent with those of planetary interiors:Em∼ E ≤ 1, β ∼ E½, ò ∼ E−1, S ∼ 1, whereE, Em'β, òandSare, respectively, the Ekman number, the magnetic Ekman number, the reciprocal square of the Alfvén Mach number, the Prandtl number and the stratification number [see definitions just after (2.22)]. The linearized basic equations for axisymmetric fluid motion are solved by boundary layer analysis. Three kinds of end-plate boundary layers and two kinds of side-wall boundary layers are found to exist. The non-diffusive interior flow is solved by Fourier-Bessel expansion method combined with Laplace transformation. The Laplace transform solution is inverted numerically by the use of residue theorem combined withMathematica(Wolfram Res., 1992). Results show that the spin-up process is finished within the homogeneous non-magnetic spin-up timet = (L2/ νΩ)½even for cases with non-negligible stratification in accordance with those of Loper's conjecture (Loper, 1976b,c).