A local magnetic equilibrium model is presented, with finite inverse aspect ratio and up–down asymmetrically shaped cross section, that depends on eight free parameters. In contrast with other local equilibria, which provide simple magnetic-surface parametrisations at the cost of complex poloidal-field flux descriptions, the proposed model is intentionally built to afford analytically tractable magnetic-field components. Therefore, it is particularly suitable for analytical assessments of equilibrium-shaping effects on a variety of tokamak-plasma phenomena.