<p>Monolayered pantographic waveguides are mechanical apparatus consisting of flexible elements hinge-connected in a diamond shape, that store elastic deformation energy on stretch gradients and exhibit an extensible-to-inextensible transition in tension. This yields exotic dispersion properties and leaves room to the hypothesis that elastic solitary waves may propagate through these waveguides. The present communication delves into this issue by exploiting a homogenized continuum description based on Hookean interaction potentials at the micro-scale—where flexible elements are considered to be inextensible—to derive admissibility conditions for solitary wave propagation. It is found that monolayered pantographic waveguides admit elastic rarefaction solitary waves. Solitary waveforms and their spectral stability are analyzed numerically.</p>