Stalk strength is an important trait in maize (Zea mays L.). Strong stalks reduce lodging and maximize harvestable yield. Studies show rind penetrometer resistance (RPR), or the force required to pierce a stalk rind with a spike, is a valid approximation of strength. We measured RPR across 4,692 recombinant inbreds (RILs) comprising the maize nested association mapping (NAM) panel derived from crosses of diverse inbreds to the inbred, B73. An intermated B73×Mo17 family (IBM) of 196 RILs and a panel of 2,453 diverse inbreds from the North Central Regional Plant Introduction Station (NCRPIS) were also evaluated. We measured RPR in three environments. Family-nested QTL were identified by joint-linkage mapping in the NAM panel. We also performed a genome-wide association study (GWAS) and genomic best linear unbiased prediction (GBLUP) in each panel. Broad sense heritability computed on a line means basis was low for RPR. Only 8 of 26 families had a heritability above 0.20. The NCRPIS diversity panel had a heritability of 0.54. Across NAM and IBM families, 18 family-nested QTL and 141 significant GWAS associations were identified for RPR. Numerous weak associations were also found in the NCRPIS diversity panel. However, few were linked to loci involved in phenylpropanoid and cellulose synthesis or vegetative phase transition. Using an identity-by-state (IBS) relationship matrix estimated from 1.6 million single nucleotide polymorphisms (SNPs) and RPR measures from 20% of the NAM panel, genomic prediction by GBLUP explained 64±2% of variation in the remaining RILs. In the NCRPIS diversity panel, an IBS matrix estimated from 681,257 SNPs and RPR measures from 20% of the panel explained 33±3% of variation in the remaining inbreds. These results indicate the high genetic complexity of stalk strength and the potential for genomic prediction to hasten its improvement.