Projects Often Experience Cost Overruns Due To Market Uncertainty And Price Escalations. Traditional Cost Estimation Methods That Rely On Point Estimation Are Incapable Of Providing Prediction Intervals As Well As Probabilistic Assessment. Thus, There Is Need For An Innovative Approach To Predict The Changes And Uncertainties In Construction Material Costs. This Paper Proposes A Novel Stochastic Model To Estimate Construction Material Costs By Applying Probabilistic Forecasting Using Autoregressive Recurrent Networks. First, Price Data Was Collected For Four Different Construction Materials. Second, Data Was Divided Into A Training Set (Pre-COVID-19) And A Testing Test (Post-COVID-19). Third, The State-Of-The-Art DeepAR Algorithm Was Implemented To Provide Probabilistic Forecasts For Construction Material Prices Under Uncertain Post-COVID Market Conditions. The Results Showed That The Proposed Stochastic Model Provides Accurate Cost Estimates With A Mean Absolute Percentage Error Of 1% For Concrete Products, Of 2% For Concrete Ingredients, Of 3% For Paving Mixtures And Blocks, And Of 4% For Steel And Iron Materials. This Paper Adds To The Body Of Knowledge By Proposing A New Approach For Estimating Construction Material By Providing Probabilistic Forecasts In The Form Of Monte Carlo Samples That Can Be Used To Compute Quantile Estimates, Which Offers Better Protections Against Rising Costs.