Sleep is the essential part of life. Thousands of people are suffering from different kinds sleep disorders. Clinical diagnosing and treating for such disorders are costly, painful and quite sluggish. To reach the demand many commercial products are into the market to encourage home based sleep studies using portable devices. These portable devices are limited in use, cannot be handled easily and quite costly. Advancements in technology miniaturized these portable devices to wearable devices to make them convenient and economical. Elastic, soft and thin silicon membrane with physical properties well matched with that of the epidermis provides conformal and robust contact with the skin. Integration of an elastic and flexible electronics to such a membrane provides an epidermal electronic system (EES) that can enhance the robustness in operation for electrophysiological signal measurement. Biocompatible and non-invasive over the skin are the advantages of this class of technology that lie beyond those available with conventional, point-contact electrode interfaces to the skin. Recording of various long-term physiological signals relevant in various sleep studies can be performed using this multifunctional device. Optimized design of EES for monitoring various physiological signals like surface electroencephalography (EEG), electrooculography (EOG) and electromyography (EMG) are presented in this project.