Predicting the stance of a text is challenging but crucial for understanding public opinion. Stance intensity detection goes beyond stance polarity prediction by classifying the stance of a text into finer-grained categories, providing a more detailed reflection of public opinion. To the best of our knowledge, most research on stance detection typically focuses on stance polarity prediction. In this work, we aim to predict both the intensity and polarity of social media posts. We conduct experiments on a recent stance intensity detection dataset comprising Reddit entries, in addition to a well-known stance (polarity) detection dataset of tweets. Using these two datasets, we carry out tests with several machine learning models, such as Support Vector Machine, Multinomial Naive Bayes, Logistic Regression, and Random Forest, and compare their accuracy and F1-score rates. Additionally, we fine-tuned a BERT model to observe its capabilities for the stance intensity detection problem on the datasets. Our study is among the initial studies that target at the important and recent problem of stance intensity detection on social media.