The thermodynamic analysis of thermoelectric devices (TEs) discards the impact caused by heat leak between source and sink. It could lead towards the partial/incomplete modelling of TEs along with some analytical gaps in their performance evaluation. Conversely, appropriate agreement among different design constraints of TEs is a must to upgrade their operating characteristics. In view of this, the modelling of multi-element single-stage thermoelectric generator (TEG) and thermoelectric heat pump (TEHP) is carried out in matrix laboratory (MATLAB 9.2). The irreversibilities caused by heat leak between the source/sink along with Fourier/Joule effects are considered for the modelling and analysis. The power output/thermal efficiency and heating capacity/coefficient of performance (COP) of TEs are analytically derived and optimized on the basis of finite time thermodynamic principles. The predetermined thermoelectric couples are chosen to maximize the heating capacity/COP in proposed configurations. Moreover, the influence of design variables viz electrical current, thermoelectric couples on system throughput is analyzed and presented. The effects of geometrical parameters viz length and area of individual modules on the performance of TEG and TEHP are also discussed.