The mouse serves as a mammalian model for understanding the nature of variation from new mutations, a question that has both evolutionary and medical significance. Previous studies suggest that the rate of single nucleotide mutations (SNMs) in mice is approximately 50% of that in humans. However, information largely comes from studies involving the C57BL/6 strain, and there is little information from other mouse strains. Here, we study the mutations that accumulated in 59 mouse lines derived from four inbred strains that are commonly used in genetics and clinical research (BALB/cAnNRj, C57BL/6JRj, C3H/HeNRj, and FVB/NRj), maintained for 8-9 generations by brother-sister mating. By analysing Illumina whole-genome sequencing data, we estimate that the average rate of new SNMs in mice is approximately $\mu = 6.7 \times 10^{-9}$. However, there is substantial variation in the spectrum of SNMs among strains, so the burden from new mutations also varies among strains. For example, the FVB strain has a spectrum that is markedly skewed towards C→A transversions, and is likely to experience a higher deleterious load than other strains, due to an increased frequency of nonsense mutations in glutamic acid codons. Finally, we observe substantial variation in the rate of new SNMs among DNA sequence contexts, CpG sites and their adjacent nucleotides playing an important role.