We examine the shape of droplets atop deformable thin elastomeric films prepared with an anisotropic tension. As the droplets generate a deformation in the taut film through capillary forces, they assume a shape that is elongated along the high tension direction. By measuring the contact line profile, the tension in the membrane can be completely determined. Minimal theoretical arguments lead to predictions for the droplet shape and membrane deformation that are in excellent agreement with the data. On the whole, the results demonstrate that droplets can be used as probes to map out the stress field in a membrane. DOI: 10.1103/PhysRevLett.118.198002 The physics of liquid droplets in contact with soft or deformable solids, elastocapillarity, is an active subject of research. Between capillary origami and wrinkling instabilities of thin films [1][2][3][4][5][6][7][8][9], the bending, coiling, and winding of slender structures [10][11][12][13][14][15][16], and elasticitymediated propulsion of droplets [17][18][19], there is no shortage of complexity, self-assembly, or beautiful examples of pattern formation in the field. In addition, some recent results have forced us to question familiar concepts of solid-liquid interactions. For instance, studies on the partial wetting of liquid drops on soft solids show that Young's law is applicable on length scales much larger than the bulk elastocapillary length γ=E, where γ is the liquid-air surface tension and E is the Young's modulus of the solid. However, on smaller length scales, the contact line reveals a wetting ridge set by a Neumann construction involving surface stresses [20][21][22][23][24][25][26].Partial wetting on deformable substrates may also be studied by employing a highly compliant geometry, such as a droplet on a thin freestanding film [27][28][29][30][31]. These studies have considered clamped films which are held taut and support a uniform and isotropic tension. As shown in Fig. 1(a), the Laplace pressure of the droplet creates a bulge in the film below it, in the shape of a spherical cap, which is of the same order in size as the droplet itself. The deformations generated may be orders of magnitude larger than the bulk elastocapillary length, because stretching of the membrane is the relevant mode of elasticity [28][29][30][31]. The contact line profile is determined by a Neumann construction, which incorporates both mechanical and interfacial tensions. This profile is characterized by the angles subtended by the liquid (θ d ) and bulge (θ b ) to the surrounding film [ Fig. 1(a)], which remains completely flat, i.e., the film's angle relative to the horizontal θ m ¼ 0. From the Neumann construction, these angles are set by two parameters: the Young's angle θ Y of the same solid supported on a rigid substrate and the ratio T in =γ, where T in is the total mechanical and interfacial tension acting inside the contact region of the membrane or drop system [31]. In the limit of infinite tension, the bulge vanishes and Young's law is recovered.In this stud...