Environmental Sound Classification (ESC) is a challenging field of research in non-speech audio processing. Most of current research in ESC focuses on designing deep models with special architectures tailored for specific audio datasets, which usually cannot exploit the intrinsic patterns in the data. However recent studies have surprisingly shown that transfer learning from models trained on ImageNet is a very effective technique in ESC. Herein, we propose SoundCLR, a supervised contrastive learning method for effective environment sound classification with state-of-the-art performance, which works by learning representations that disentangle the samples of each class from those of other classes. Our deep network models are trained by combining a contrastive loss that contributes to a better probability output by the classification layer with a cross-entropy loss on the output of the classifier layer to map the samples to their respective 1-hot encoded labels. Due to the comparatively small sizes of the available environmental sound datasets, we propose and exploit a transfer learning and strong data augmentation pipeline and apply the augmentations on both the sound signals and their log-mel spectrograms before inputting them to the model. Our experiments show that our masking based augmentation technique on the log-mel spectrograms can significantly improve the recognition performance. Our extensive benchmark experiments show that our hybrid deep network models trained with combined contrastive and cross-entropy loss achieved the state-of-the-art performance on three benchmark datasets ESC-10, ESC-50, and US8K with validation accuracies of 99.75\%, 93.4\%, and 86.49\% respectively. The ensemble version of our models also outperforms other top ensemble methods. The code is available at https://github.com/alireza-nasiri/SoundCLR.