Cluster-spin glass and ferroelectric relaxors have been observed in defect-containing ferromagnetic systems and ferroelectric systems, respectively. However, it is unclear whether or not an analogous glass state exists in the physically parallel ferroelastic (or martensitic) systems. In the 1990s, theoretical studies suggested that premartensitic tweed could be viewed as a strain glass. However, there has been no experimental verification of this hypothesis. In this paper, we provide an experimental test of this hypothesis by measuring the possible glass signatures in two well-known premartensitic tweed systems prior to their martensitic transformation: one Ni₆₃Al₃₇ and the other Ti₅₀Ni₄₇Fe₃ martensitic alloy. Our experiments show that no glass signatures exist for the premartensitic tweed in both systems. There is no mechanical susceptibility/modulus anomaly in the tweed temperature regime, suggesting no glass transition exists. The tweed remains ergodic, inconsistent with a frozen glass. These two critical experiments show that premartensitic tweed is not a frozen glass state. We demonstrate that strain glass exists in ferroelastic/martensitic systems but only in defect-containing ferroelastic/martensitic systems with defect concentration exceeding a critical value. This strain glass is a mechanical analogue of cluster-spin glass or ferroelectric relaxors, and possesses all the features of a glass. We further show that the tweed is equivalent to an ‘unfrozen state’ of a strain glass. Finally, we demonstrate that the microscopic origin of the strain glass can be easily understood in analogy with the behavior of a ‘defect-containing domino array’.