We　investigate　the　relationship　between　the　eigenvalues　of　a　graph　G　and　fractional　spanning　tree　packing　and　coverings　of　G.　Let　ω(G)　denote　the　number　of　components　of　a　graph　G.　The　strength　η(G)　and　the　fractional　arboricity　γ(G)　are　defined　by　η(G)=min,　where　the　optima　are　taken　over　all　edge　subsets　X　whenever　the　denominator　is　non-zero.　The　well　known　spanning　tree　packing　theorem　by　Nash-Williams　and　Tutte　indicates　that　a　graph　G　has　k　edge-disjoint　spanning　tree　if　and　only　if　η(G)≥k;　and　Nash-Williams　proved　that　a　graph　G　can　be　covered　by　at　most　k　forests　if　and　only　if　γ(G)≤k.　Let　λi(G)　(μi(G),　qi(G),　respectively)　denote　the　ith　largest　adjacency　(Laplacian,　signless　Laplacian,　respectively)　eigenvalue　of　G.　In　this　paper,　we　prove　the　following.　(1)　Let　G　be　a　graph　with　δ≥2s/t.　Then　η(G)≥s/t　if　μn−1(G)>,　or　if　λ2(G)<δ−.　(2)　Suppose　that　G　is　a　graph　with　nonincreasing　degree　sequence　d1,d2,…,dn　and　n≥⌊⌋+1.　Let　β=⌋+1di.　Then　γ(G)≤s/t,　if　β≥1,　or　if　0<β<1,　n>⌊2s/t⌋+1+.　Our　result　proves　a　stronger　version　of　a　conjecture　by　Cioabă　and　Wong　on　the　relationship　between　eigenvalues　and　spanning　tree　packing,　and　sharpens　former　results　in　this　area.　©　2016　Elsevier　B.V.