Efficiency of any machining process depends on the effectiveness of final outcomes. Surface integrity plays an important role in functional performance of a part or component. Traditionally, surface roughness is considered to be the principal parameter to assess the surface integrity of a machined surface. In this paper, the influences of machining parameters like gap voltage, capacitance and depth of hole on the surface finish parameters like Ra and Sa of micro holes have been studied in micro electrical discharge drilling. The high aspect ratio blind micro holes were drilled on titanium alloy (Ti-6Al-4V) with cylindrical tungsten tool electrodes. The experimentation was carried out adopting a full factorial design (33). The simultaneous effects of machining parameters on responses were analysed using response surface methodology. Multiple linear regression models were developed for responses to obtain the correlation between machining parameters and machining outputs. Multi-objective optimization has been performed with the aid of the desirability function approach.