During embryonic development and wound healing, the mechanical signals transmitted from cells to their neighbors induce tissue rearrangement and directional movements. It has been observed that forces exerted between cells in a developing tissue under stress are not always monotonically varying, but they can be pulsatile. Here we investigate the response of model tissues to controlled external stresses. Spherical cellular aggregates are subjected to one-dimensional stretching forces using micropipette aspiration. At large enough pressures, the aggregate flows smoothly inside the pipette. However, in a narrow range of moderate aspiration pressures, the aggregate responds by pulsed contractions or “shivering.” We explain the emergence of this shivering behavior by means of a simple analytical model where the uniaxially stretched cells are represented by a string of Kelvin–Voigt elements. Beyond a deformation threshold, cells contract and pull on neighboring cells after a time delay for cell response. Such an active behavior has previously been found to cause tissue pulsation during dorsal closure of Drosophila embryo.