The purposes of this study are to determine the effects of baricitinib on the time it takes to remove simvastatin from the body and to look at how well-tolerated and safe baricitinib is when given alone and in combination with simvastatin. Side effects will be documented. The study will last approximately 7 days from the first dose to the end of the study (not including screening or follow-up).

Inclusion Criteria:

• Male participants - Agree to use 2 reliable methods of birth control with female partners of childbearing potential during the study and for at least 3 months following the last dose of study drug
• Female participants - Women not of childbearing potential due to surgical sterilization confirmed by medical history, or menopause
• Have a body mass index of 18.0 to 29.0 kilograms per meter squared (kg/m^2), inclusive
• Have clinical laboratory test results within the normal reference range
• Have normal renal function
• Have normal blood pressure and pulse rate

Exclusion Criteria:

• Are currently enrolled in a clinical trial involving a study drug or off-label use of a drug or device, or are concurrently enrolled in any other type of medical research
• Have completed or discontinued within the last 90 days from a clinical trial involving a study drug
• Have previously completed or withdrawn from this study or any other study investigating baricitinib, and have previously received baricitinib
• Have known allergies to baricitinib, simvastatin, related compounds, or any components of the baricitinib or simvastatin formulations, or history of significant atopy
• Have an abnormality in the 12-lead electrocardiogram (ECG)
• Have a history of, or current cardiovascular, respiratory, hepatic, renal, gastrointestinal, endocrine (including hypothyroidism), hematological, or neurological disorders
• Have current or recent history of myalgia or muscle weakness
• Regularly use known drugs of abuse and/or show positive findings on urinary drug screening
• Have a current or recent history of a clinically significant bacterial, fungal, parasitic, viral (not including rhinopharyngitis), or mycobacterial infection
• Have had symptomatic herpes zoster or herpes simplex infection within 90 days prior to the first dose
• Have an absolute neutrophil count (ANC) less than 2 × 10^9/liters (L) [2000 cells/microliter (μL)] at screening or day prior to first dose of study drug. For abnormal values, a single repeat will be allowed
• Show evidence of human immunodeficiency virus (HIV) infection and/or positive human HIV antibodies
• Show evidence of hepatitis C infection and/or positive hepatitis C antibody
• Show evidence of hepatitis B infection and/or positive hepatitis B surface antigen
• Are women who are lactating
• Have been exposed to a live vaccine within 12 weeks prior to the first dose or expected to need/receive a live vaccine (including herpes zoster vaccination) during the course of the study
• Intend to use over-the-counter or prescription medication (including salicylate drugs) and/or herbal supplements within 14 days prior to dosing and during the study or intended use of vitamin supplements from Day 1 until discharge from the Clinical Research Unit (CRU)
• Have consumed or intend to consume grapefruit or grapefruit-containing products within 14 days prior to the first dose and throughout the study
• Have donated or lost blood of more than 500 milliliters (mL) within the last 3 months
• Have an average weekly alcohol intake that exceeds 28 units per week (males) and 21 units per week (females), or are unwilling to stop alcohol consumption from 48 hours prior to the first dose until discharge from the CRU at the end of Period 2
• History of, in the opinion of the investigator, excessive methylxanthine use within the previous 6 months, such as greater than (>)6 cups of coffee (or equivalent) per day
• Currently smoke more than 10 cigarettes per day

All enrolled participants.

Baseline through study completion (up to Day 18)