The increasing ageing population around the world, is calling for technological innovations that can improve the lives of elderly people. Real time monitoring their activities is imperative in order to mitigate the detrimental occurrences and dangerous events like falls. The aim of this research is to develop and test a Machine Learning model, capable to determine the activity performed by the elderly in their everyday environment. Data for this research was acquired by setting up two fully monitored rooms, equipped with Radio Frequency Identification (RFID) antennas, while subjects who participated in the experiment were wearing a Wearable Wireless Identification and Sensing Platform (W2ISP) tag. The dataset consisted of 14 healthy elders, who would perform four activities namely: sitting on the bed, sitting on a chair, lying in bed and ambulating. Nine independent variables were used, eight of which were obtained by the sensors as raw data vectors and the ninth is the gender. The final data set includes 75,128 records. Totally, 25 Classification Algorithms were used in an effort to determine the more efficient model. The best performance has been achieved by employing the Bagged Trees algorithm. A combination of 10-fold Cross validation and Grid Search was used in order to tune the values of the hyperparameters and to avoid any form of overfitting or underfitting. The accuracy and the generalization ability of the optimal model, have been proved by the high values of all performance indices, with a very small deviation for the case of the fourth activity. Thus, this approach can be reliably used (with low cost) by caregivers, hospital staff or anyone else in charge, to watch for potentially dangerous situations for the elders.