We have investigated anharmonic behavior of Pd by applying systematic nanoscale tensile testing to near defect-free nanowhiskers offering a large range of elastic strain. We measured size-dependent deviations from bulk elastic behavior in nanowhiskers with diameters as small as ∼30  nm. In addition to size-dependent variations in Young’s modulus in the small strain limit, we measured nonlinear elasticity at strains above ∼1%. Both phenomena are attributed to higher-order elasticity in the bulklike core upon being biased from its equilibrium configuration due to the role of surface stresses in small volumes. Quantification of the size-dependent second- and third-order elastic moduli allows for calculation of intrinsic material nonlinearity parameters, e.g., δ. Comparison of the size-independent values of δ in our nanowhiskers with studies on bulk fcc metals lends further insight into the role of length scales on both elastic and plastic mechanical behavior.