Bronze grave markers that are relatively new can be wiped clean with a damp cloth. At this stage, cleaning doesn't require the use of chemicals. Cleaning a weathered bronze grave marker is done with a soft cloth and a cleaning agent such as mineral oil, Armor-All or WD-40.
To scrub dirt and debris off of a bronze grave marker, use a brush with nylon bristles. A toothbrush is ideal for removing embedded dirt between letters and decorative accents. Bring a bucket of water to rinse the marker after washing. Dry the marker with a soft towel, taking special care to remove residual oil from lettering. Finish with a light application of WD-40 to protect the marker from the elements.