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We present a simple physically based quantitative model of blood platelet shape and its evolution during agonist-induced activation. The model is based on the consideration of two major cytoskeletal elements: the marginal band of microtubules and the submembrane cortex. Mathematically, we consider the problem of minimization of surface area constrained to confine the marginal band and a certain cellular volume. For resting platelets, the marginal band appears as a peripheral ring, allowing for the analytical solution of the minimization problem. Upon activation, the marginal band coils out of plane and forms 3D convoluted structure. We show that its shape is well approximated by an overcurved circle, a mathematical concept of closed curve with constant excessive curvature. Possible mechanisms leading to such marginal band coiling are discussed, resulting in simple parametric expression for the marginal band shape during platelet activation. The excessive curvature of marginal band is a convenient state variable which tracks the progress of activation. The cell surface is determined using numerical optimization. The shapes are strictly mathematically defined by only three parameters and show good agreement with literature data. They can be utilized in simulation of platelets interaction with different physical fields, e.g. for the description of hydrodynamic and mechanical properties of platelets, leading to better understanding of platelets margination and adhesion and thrombus formation in blood flow. It would also facilitate precise characterization of platelets in clinical diagnosis, where a novel optical model is needed for the correct solution of inverse light-scattering problem., Author summary Blood platelets are the second most numerous component of blood after red blood cells. Their main function is to stop bleeding upon vessel wall injury. Contact with foreign substances, normally absent inside the bloodstream, leads to platelet activation. After this, platelets adhere to the damaged surface and to each other, finally forming a mechanical plug. Activation is very fast and complex process, and is accompanied by dramatic change of cell shape. This morphological alteration may be vital for the prevention of blood loss. However, there is no complete understanding of its significance, maybe because the quantitative description of the platelet shape during activation is absent. Here, we describe the shape change based on the physical consideration of the platelet cytoskeleton. We propose the formulation of mathematical problem and its solution, which allows one to easily simulate a wide class of shapes for both resting and activated cells. These models are in a good agreement with platelet images observed in numerous experiments published elsewere. They may be used to simulate the shape change and hence the influence of activation on hydrodynamic, mechanical and optical properties of platelets. As a result, novel diagnostic and therapeuthic strategies and clinical implications may be obtained.