Mechanical properties of soft biological tissues play a key role in their normal physiology, contributing to their formation during development, maintenance and repair during adult homeostasis, and driving diseases such as cancer. Mechanics has been proposed to exert its effect by impacting cells fate decisions and cell behaviours including proliferation, differentiation and motility, amongst others. However, despite its critical relevance, a comprehensive analysis of the biomechanics of soft biological tissues is still lacking due to the limitations of the existing characterisation tools. In this article, we describe the development of a device for uniaxial tensile testing of small samples of epithelial and connective tissues, based on the closed-loop interaction between an electromagnetic force actuator and an optical strain sensor. First, we validate the device with synthetic elastomers of known mechanical properties and compare its performance with conventional tensile testing methods; then, we characterise the mechanical properties of the squamous epithelium of the mouse oesophagus along with its supporting connective tissue and underlying muscle in controlled environmental conditions. Through an analysis of strain-stress curves, we demonstrate that the whole oesophagus behaves as a trilayered composite material, whose overall mechanical response depends on the properties of each of its tissue layers. Overall, the proposed setup enables measurements of the mechanical properties of soft biological tissues with unprecedented reliability and precision, and offers an ideal platform for future instrument developments.