During storage, many apple (Malus ×domestica Borkh.) genotypes lose their desirable textural qualities, but some like `Honeycrisp', maintain their sensory Crispness and Firmness. To understand this differential response of genotypes to postharvest changes in texture, reliable and quantifiable methods of texture measurement are needed. This study integrated data from a snapping test, confocal laser scanning microscopy (CLSM), and sensory panels to study postharvest textural changes and to predict sensory textural attributes of Firmness, Crispness, Mealiness, and Juiciness. Three separate analyses on fresh, stored, and combined fresh and stored fruit data yielded different predictors for the same sensory attributes. Change in Crispness during storage was successfully predicted by change in Work during storage. Cell number and size were related to fresh fruit texture and its maintenance during storage. Unique textural properties of `Honeycrisp' were found to be inherited by its progeny.