Cell constriction is a decisive step for division in many cells. However, its physical pathway remains poorly understood, calling for a quantitative analysis of the forces required in different cytokinetic scenarios. Using a model cell composed by a flexible membrane (actin cortex and cell membrane) that encloses the cytoplasm, we study the mechanical conditions necessary for stable symmetric constriction under radial equatorial forces using analytical and numerical methods. We deduce that stable symmetric constriction requires positive effective spontaneous curvature, while spontaneous constriction requires a spontaneous curvature higher than the characteristic inverse cell size. Surface tension reduction (for example by actin cortex growth and membrane trafficking) increases the stability and spontaneity of cellular constriction. A reduction of external pressure also increases stability and spontaneity. Cells with prolate lobes (elongated cells) require lower stabilization forces than oblate-shaped cells (discocytes). We also show that the stability and spontaneity of symmetric constriction increase as constriction progresses. Our quantitative results settle the physical requirements for stable cytokinesis, defining a quantitative framework to analyze the mechanical role of the different constriction machinery and cytokinetic pathways found in real cells, so contributing to a deeper quantitative understanding of the physical mechanism of the cell division process.