The remote monitoring of the elderly and patients with diseases that promote physical weakness are a relevant trend in healthcare. This work presents a smartphone based tool to assist these people, which is capable for detecting a fall of monitored patient and to alert the responsible, enabling an agile medical assistance. Moreover, we analyzed and implemented machine learning algorithms to increase the accuracy of the monitoring process, in order to avoid false alarms and fall detection misses. The initial results show that the selected algorithms provide better results than models based on smartphone's accelerometer upper and lower thresholds to trigger the fall alarms, which are the main approaches observed in the literature.