Identifying crop loss at field parcel scale using satellite images is challenging: first, crop loss is caused by many factors during the growing season; second, reliable reference data about crop loss are lacking; third, there are many ways to define crop loss. This study investigates the feasibility of using satellite images to train machine learning (ML) models to classify agricultural field parcels into those with and without crop loss. The reference data for this study was provided by Finnish Food Authority (FFA) containing crop loss information of approximately 1.4 million field parcels in Finland covering about 3.5 million ha from 2000 to 2015. This reference data was combined with Normalised Difference Vegetation Index (NDVI) derived from Landsat 7 images, in which more than 80% of the possible data are missing. Despite the hard problem with extremely noisy data, among the four ML models we tested, random forest (with mean imputation and missing value indicators) achieved the average AUC (area under the ROC curve) of 0.688±0.059 over all 16 years with the range [0.602, 0.795] in identifying new crop-loss fields based on reference fields of the same year. To our knowledge, this is one of the first large scale benchmark study of using machine learning for crop loss classification at field parcel scale. The classification setting and trained models have numerous potential applications, for example, allowing government agencies or insurance companies to verify crop-loss claims by farmers and realise efficient agricultural monitoring.