Extra-large deformations in ultra-soft elastic materials are ubiquitous, yet systematic studies and methods to understand the mechanics of such huge strains are lacking. Here we investigate this complex problem systematically with a simple experiment: by introducing a heavy bead of radius a in an incompressible ultra-soft elastic medium. We find a scaling law for the penetration depth (δ) of the bead inside the softest gels as δ ∼ a 3/2 which is vindicated by an original asymptotic analytic model developed in this article. This model demonstrates that the observed relationship is precisely at the demarcating boundary of what would be required for the field variables to either diverge or converge. This correspondence between a unique mathematical prediction and the experimental observation ushers in new insights into the behavior of the deformations of strongly non-linear materials. 83.85.Cg,46.05.+b,83.80.Va Singularities are pervasive in various problems of linear continuum mechanics. In wetting, stress diverges at a moving contact line [1,2]; it diverges at the tip of a crack or even at a sharp point indenting a plane [3]. Understanding how such singularities can be tempered has often given rise to new physics invariably prompting us, on many occasions, to investigate a material phenomenon at a molecular dimension and then herald a way to bridge the near field with the far field behavior in a rather non-trivial manner. Nature, however, performs the difficult task herself and leaves her signature in a way that is independent of the constitutive property of a material, yet it belongs to a class of universality. What we report here is such a universality that is discovered in the large deformation behavior of ultra-soft gels. Soft solids undergoing huge deformations exhibit various fascinating and puzzling mechanical behaviors [4][5][6][7][8][9][10][11][12][13][14][15]. Our experimental protocol to study extra-large elastic deformations is remarkably simple, in that a heavy bead of stainless steel is gently deposited on the horizontal flat surface of a gel. The compliant gel is deformed by the load exerted by the heavy bead. It reaches a stable (elasto-buoyant) equilibrium position when the elastic force exerted by the surrounding gel balances its weight [14], within few tenths of a second. This experiment can be viewed as an elastic analog of the falling ball viscometry, in which the bead reaches a terminal sedimentation velocity resulting from the balance of the bead's weight and the viscous drag force [16]. In the limit of Hookean elasticity, an analogy with the Stokes equation (by replacing shear viscosity with shear modulus and velocity with depth of submersion, δ) [17] suggests that δ ∼ a 2 , a being the sphere radius. While for the higher modulus gels (Fig.1-a), such a relationship is more or less valid, for the softer ones, when the bead is totally engulfed by the gel and the deformations are very large ( Fig.1-b), it is observed that the depth scales with the bead's radius with an exponent of 3/2. This...