Shape is an important passive marker in label-free particle and cell separation for chemical, biomedical, and environmental applications. We demonstrate herein a continuous-flow shape-based separation of spherical and peanut-shaped rigid particles of equal volume (or equivalent spherical diameter) via elasto-inertial pinched flow fractionation (eiPFF). This microfluidic technique exploits the shape dependence of the flow-induced elasto-inertial lift (and hence the cross-stream migration) in viscoelastic fluids to increase the displacement of a sheath flow-focused particle mixture for a high-purity separation. The parametric effects on this shape-based particle separation via eiPFF are systematically investigated in terms of five dimensionless numbers. It is found that the separation is strongly affected by the flow rate, fluid elasticity, and channel aspect ratio. Interestingly, the elasto-inertial deflection of the peanut particles can be either greater or smaller than that of equally volumed spherical particles. This phenomenon is speculated to correlate with the rotational effects of peanut particles.