Серверный:

    public HttpResponseMessage Post([FromUri]string machineName)
    {
        HttpResponseMessage result = null;
        var httpRequest = HttpContext.Current.Request;

        if (httpRequest.Files.Count > 0 && !String.IsNullOrEmpty(machineName))
        ...

Сторона клиента:

    public static void PostFile(string url, string filePath)
    {
        if (String.IsNullOrWhiteSpace(url) || String.IsNullOrWhiteSpace(filePath))
            throw new ArgumentNullException();

        if (!File.Exists(filePath))
            throw new FileNotFoundException();

        using (var handler = new HttpClientHandler { Credentials=  new NetworkCredential(AppData.UserName, AppData.Password, AppCore.Domain) })
        using (var client = new HttpClient(handler))
        using (var content = new MultipartFormDataContent())
        using (var ms = new MemoryStream(File.ReadAllBytes(filePath)))
        {
            var fileContent = new StreamContent(ms);
            fileContent.Headers.ContentDisposition = new ContentDispositionHeaderValue("attachment")
            {
                FileName = Path.GetFileName(filePath)
            };
            content.Add(fileContent);
            content.Headers.ContentType = new MediaTypeHeaderValue("application/octet-stream");

            var result = client.PostAsync(url, content).Result;
            result.EnsureSuccessStatusCode();
        }
    }   

На стороне сервера коллекция httpRequest.Files всегда пуста. Но заголовки (длина содержимого и т. Д.) Верны.