We in this paper exploit time series algorithm based deep learning in forecasting damage mechanics problems. The methodologies that are able to work accurately for less computational and resolving attempts are a significant demand nowadays. Relied on learning an amount of information from given data, the long short-term memory (LSTM) method and multi-layer neural networks (MNN) method are applied to predict solutions. Numerical examples are implemented for predicting fracture growth rates of L-shape concrete specimen under load ratio, single-edge-notched beam forced by 4-point shear and hydraulic fracturing in permeable porous media problems such as storage-toughness fracture regime and fracture-height growth in Marcellus shale. The predicted results by deep learning algorithms are well-agreed with experimental data.